Practice Test

Q1) Two events A and B are said to be incompatible when Show Answer

Q2) The first application of probability was done in Show Answer

Q3) Initially probability was a branch of Show Answer

Q4) Now probability is an integral part of Show Answer

Q5) The two divisions of probability are Show Answer

Q6) Subjective probability is based on Show Answer

Q7) Subjective probability is used in the field of Show Answer

Q8) An experiment is said to be Random experiment if Show Answer

Q9) The result of an experiment is called Show Answer

Q10) The two types of events are: Show Answer

Q11) The events which can be decomposed into two or more events is called: Show Answer

Q12) Two events A and B are called mutually symmetric events Show Answer

Q13) The limitation of Priori definition of probability is Show Answer

Q14) P(A) + P(A') = Show Answer

Q15) Classical definition is used in case of tossing coin, throwing dice, etc. Show Answer

Q16) Odds in favour of events are 5:4. Therefore probability of that events is Show Answer

Q17) The probability of an event is 9/16. Therefore odds against an event is Show Answer

Q18) A and A' and are mutually exclusive events Show Answer

Q19) A is called a sure event when Show Answer

Q20) A is an impossible events when Show Answer

Q21) A coin is tossed 2 times. The odds against at least 1 head is Show Answer

Q22) A - B = Show Answer

Q23) A' = Show Answer

Q24) P(A or B ) = Show Answer

Q25) P ( A or B) = ____________
when A and B are mutually Show Answer

Q26) A and B are independent events. Therefore A and B' are also independent event Show Answer

Q27) Value assigned to Random variable is from the set of: Show Answer

Q28) Number of misprints, number of tire bursting, etc. are example of: Show Answer

Q29) Height, Marks, Age are example of Show Answer

Q30) The probability of getting score 5 at least once when the die is thrown thrice Show Answer

Q31) The odds of in favour of getting a king card when a card is drawn from the pack Show Answer

Q32) When two coin are tossed simultaneously then the probability of getting atmost one head is Show Answer

Q33) For a random variable its variance is 5 then variance for (-3x +7) is Show Answer

Q34) The expected value of a random variance is always Show Answer

Q35) When 2 dice are thrown the probablility of getting the sum of the score as a perfect square is Show Answer

Q36) Two dice are thrown the probability of getting at a test are 3:7. The odds against another student passing at are 3: 5. What are the odds that both fail? Show Answer

Q37) Two dice are thrown the probability of getting at a test are 3:7. The odds against another student passing at are 3: 5. What are the odds that only the 2nd student passes? Show Answer

Q38) A salesman is known to sell a product in 3 out of 5 attempts, while another salesman in 2 out of 5 attempts. Find the probability that no sale will be affected when they both try to sell the product. Show Answer

Q39) A salesman is known to sell a product in 3 out of 5 attempts, while another salesman in 2 out of 5 attempts. Find the probability that either of them will succeed in selling the product. Show Answer

Q40) A company has production section viz. and which contribute 30%, 20% 28% and 22% respectively to the total output. It wsa observed that these sections respectively produced 1%, 2%, 3% and 4% defective units. If the units is selected at random and found to be defective, what is the probability that the unit so selected has come from either section one or section four? Show Answer

Q41) The chairman of a company needs to purchase three typewriters, each a different brand, for typing purposes. Five brands are available, which we call as A, B, C, D and E . If his selection of three typewriters is random, what is the probability that the three will include A and B,C and D or A, B and C . Show Answer

Q42) Two different digits are selected at random from digits 1, 2,........, 9. If the sum is odd, what is the probability that 2 is one of the digits selected? Show Answer

Q43) A committee of 4 people is to be appointed from 3 officers of the production department, 4 officers of the purchase department, 2 officers of the sales department and 1 charted accountant. Find the probability of forming the committee in which there must be one from each category. Show Answer

Q44) A committee of 4 people is to be appointed from 3 officers of the production department, 4 officers of the purchase department, 2 officers of the sales department and 1 charted accountant. Find the probability of forming the committee in which it should have at least one from the purchase department. Show Answer

Q45) A committee of 4 people is to be appointed from 3 officers of the production department, 4 officers of the purchase department, 2 officers of the sales department and 1 charted accountant. Find the probability of forming the committee where the chartered accountant must be in the committee. Show Answer

Q46) Two set of candidates are competing for the position on the Board of Directors of a company. The probability that first and second set will win are 0.6 and 0.4 respectively. If the first set wins, the probability of introducing a new product is 0.8 and the corresponding probability if the second set win is 0.3. What is the probability that the new product will be introduced? Show Answer

Q47) A and B choose a digit at random from 0, 1, 2,........,9 independently. Find the probability that the product of the two digits chosen is zero. Show Answer

Q48) A problem in statistics is given to two students A and B . The odds in favour of A solving the problem are 6 to 9 and against B solving the problem are 12 to 10. if A and B attempt, find the probability of the problem being solved. Show Answer

Q49) Suppose that it is 11 to 5 against a person who is now 38 years of age living till he is 73 and 5 to 3 against B now 43 living till he is 78 years. Find the chance that at least one of these persons will be alive 35 years hence. Show Answer

Q50) Two cards are drawn from a pack of 52 cards at random and kept out. Them one card is drawn from the remaining 50 cards. Find the probability that it is ace. Show Answer

Q51) A committee of 4 persons is to be appointed from 7 men and 3 women, what is the probability that the committee contains exactly two women. Show Answer

Q52) A person is known to hit a target in 5 out of 8 shots, whereas another person is known to hit it in 3 out of 5 shots. Find the probability that the target is not hit at all when they both try. Show Answer

Q53) A person throws an unbiased die. If the number shown is even, he gains an amount equal to the number shown. If the number is odd, he loses an amount equal to the number shown, find his expectation. Show Answer

Q54) A service station manager sells gas at an average of $100 per day on a rainy day, $150 on a 'dubious day', $250 on a fair day, and $300 on a clear day. If weather bureau Statistics show the probabilities of weather as follows, find his mathematical expectation:
Clear 0.50
Fair 0.30
Dubious 0.15
Rainy 0.05
Show Answer

Q55) A die tossed twice. If it shows the same number twice, Gopal gets Rs.100 otherwise he loses Rs.5. What is his mathematical expectation? Show Answer

Q56) A player tosses three fair coins. He wins Rs.8 if 3 heads occur, Rs.3 if 2 heads occur and Re.1 if only 1 head occurs. If the game is to fair, how much would he lose if no heads occur? Show Answer

Q57) In a business venture, a man can make a profit of Rs.2000 with a probability of 0.4 or have a loss of Rs.1000 with a probability of 0.6. What is his expected profit? Show Answer

Q58) A person tosses two coins simultaneously. He receives Rs.8 for two heads, Rs.2 for one head and he is to pay Rs.6 for no head. Find his expectation. Show Answer

Q59) A man draws 2 balls from a bag containing 3 white and 5 black balls. If he is to receive Rs.14 for every white ball and Rs.7 fore every black ball drawn, what is his expectation? Show Answer

Q60) 5000 tickets are sold in a lottery in which there is a first prize of Rs.10000, two second prizes of Rs.2000 each and 10 third prizes of Rs.200 each. One ticket cost Rs.2. find the expected net gain or loss if you buy one ticket? Show Answer

Q61) A player tosses 3 coins. He wins Rs.20 if all the three coins show head, Rs.10 if 2 coins show heads and Rs.5 if one head appears. If no head appears, he loses Rs.4. find his expectation. Show Answer

Q62) The probability that there is at least one error in an accounts statement prepared by A is 0.2 and for B and C , they are 0.25 and 0.4 respectively. A and B ,C prepared 10, 16 and 20 statements respectively. Find the expected number of correct statements in all. Show Answer

Q63) The probability that a man fishing at a particular place will catch 1, 2, 3, 4 fish are 0.1, 0.3, 0.2 and 0.4 respectively. What is the expected number of fish caught? Show Answer

Q64) A petrol pump proprietor sells an average of Rs.80000 petrol on rainy days and an average of Rs.95000 on clear days. Statistics from the Metereological Department show that the probability is 0.76 for clear weather and 0.24 for rainy weather on coming Monday. Find the expected value of petrol sale. Show Answer

Q65) A wheel of fortune art an amusement park is divided into five colours: red, blue, green, yellow, brown. The probabilities of the spinner landing in any of these colours are 3/10, 3/10, 2/10, 1/10, 1/10 respectively. A player can win Rs.5 if it stops on red, Rs.3 if it stops on blue, Rs.4 if it stops on green and lose Rs.2 if it stops on yellow and Re.1 if it stops on brown. Meena wants to try her luck. What is her mathematical expectation? Show Answer

Q66) If the probability that a man wins a prize of Rs.10 is 3/5 and the probablilty that he wins nothing is 2/5, find the mathematical expectation? Show Answer

Q67) Calculate the expected value of , the sum of the score when two dice are rolled. Show Answer

Q68) An investment consultant predicts that the odds against the price of a certain stock going up are 2 : 1 and the odds in favour of the price remaining the same are 1 : 3. what is the probability that the price of the stock will go down? Show Answer

Q69) What is the probability that a leap year selected at random will contain either 53 thusrdays or 53 Fridays? Show Answer

Q70) From a well shuffled pack of 52 cards, two are drawn at random. What are the odds against they being a king and an ace? Show Answer

Q71) A chartered accountant applies for a job in two firms X and Y , he estimates that the probability of his being selected in firm X is 0.7 and being selected at Y is 0.5 and the probability of at least one of is applications being rejected is 0.6. What is the probability that he will be selected in one of the firms? Show Answer

Q72) There are 4 letters and 4 addressed envelopes. Find the chance that all letters are not dispatched in the right envelopes. Show Answer

Q73) A certain player X is known to win with probability 0.3 if the track is fast and 0.4 if the track is slow. For Monday, there is a 0.7 probability of a fast track and 0.3 probability of a slow track. What is the probability that the player X will win on Monday? Show Answer

Q74) A pair of dice is thrown and sum of the numbers on the two dice is observed to be 6. what is the probability that there is 2 on one of the dice? Show Answer

Q75) A die is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. What is the probability that sum of the two numbers shown is even? Show Answer

Q76) An urn contains 10 counters on which digits 0, 1, 2, ......9 are written one digit on each counter, no digit being repeated. A chooses a counter first and then B chooses another counter ( the first is not replaced). Find the probability that the product of the two digits chosen in zero. Show Answer

Q77) There are four hotels in a certain town. If 3 men check into hotels in a day, what is the probability that each check into a different hotels? Show Answer

Q78) Two different digits are selected at a random from the digits 1,2,......9. If the sum is odd what is the probability that 2 is one of the digits selected? Show Answer

Q79) It is known that 40% of the students in a certain college are girls and 50% of the students are above the median height. If 2/3 of the boys are above the median height, what is the probability that a randomly selected student who is below the median height is a girl? Show Answer

Q80) Four digits 1, 2, 4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4? (Repetition is allowed) Show Answer

Q81) Anita and Binita stand in a line with 7 other people. What is the probability that there are 4 persons between them? Show Answer

Q82) Out of 80 students in a class, 30 passed in Mathematics, 20 passed in Statistics and 10 passed in both. One student is selected at random. Find the probability that he has passed at least in one of the subjects. Show Answer

Q83) Out of 80 students in a class, 30 passed in Mathematics, 20 passed in Statistics and 10 passed in both. One student is selected at random. Find the probability that he has passed none of the above subjects Show Answer

Q84) Out of 80 students in a class, 30 passed in Mathematics, 20 passed in Statistics and 10 passed in both. One student is selected at random. Find the probability that he has passed only in Maths. Show Answer

Q85) Out of 80 students in a class, 30 passed in Mathematics, 20 passed in Statistics and 10 passed in both. One student is selected at random. Find the probability that he has passed only in Statistics. Show Answer

Q86) Out of 80 students in a class, 30 passed in Mathematics, 20 passed in Statistics and 10 passed in both. One student is selected at random. Find the probability that he has passed exactly in one of the subjects. Show Answer

Q87) If x is a continuous random variable over the interval [a, b] then for f (x) to be a probability density function the conditiond are Show Answer

Q88) E(x and y) =E(x). E(y) provided Show Answer

Q89) The value E(10) is Show Answer

Q90) P(A-B) = Show Answer

Q91) P(A) = P(B) =5/9, P(A-B)=2/9 Show Answer

Q92) If x and y are 2 random variable having expected value 7 and 5 respectively the expected value of E(x+y) Show Answer

Q93) If x and y are 2 random variable such that y =8 -7x then v(y) is given by Show Answer

Q94) A wheel of fortune at an amusement park is divided into five colours: red, blue, green, yellow, brown. The probabilities of the spinner landing in any of these colours are 3/10, 3/10, 2/10, 1/10, 1/10 respectively. A player can win Rs.5 if it stops on red, Rs.3 if it stops on blue, Rs.4 if it stops on green and lose Rs.2 if it stops on yellow and Re.1 if it stops on brown. Meena wants to try her luck. What is her mathematical expectation ? Show Answer

Q95) A die is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. What is the probability that sum of the two numbers shown is even ? Show Answer

Q96) Out of 80 students in a class, 30 passed in Mathematics, 20 passed in Statistics and 10 passed in both. One student is selected at random. Find the probability that he has passed none of the above subjects Show Answer

Q97) Out of 80 students in a class, 30 passed in Mathematics, 20 passed in Statistics and 10 passed in both. One student is selected at random. Find the probability that he has passed only in Statistics. Show Answer