Related InterviewSolutions

• Let E and F be two independent events. The probability that exactly one of them occurs is `11//25` and the probability of none of them occurring is `2//25.` If P(T) denotes the probability of occurrence of the event T, thenA. `P(E)=4/5,P(F)=3/5`B. `P(E)=1/5,P(F)=2/5`C. `P(E)=2/5,P(F)=1/5`D. `P(E)=3/5,P(F)=4/5`
• Of the three independent event `E_(1),E_(2)` and `E_(3)`, the probability that only `E_(1)` occurs is `alpha`, only `E_(2)` occurs is `beta` and only `E_(3)` occurs is `gamma`. If the probavvility p that none of events `E_(1), E_(2)` or `E_(3)` occurs satisfy the equations `(alpha - 2beta)p = alpha beta` and `(beta - 3 gamma) p = 2 beta gamma`. All the given probabilities are assumed to lie in the interval (0, 1). Then, `("probability of occurrence of " E_(1))/("probability of occurrence of " E_(3))` is equal to
• Football teams `T_(1)and T_(2)` have to play two games are independent. The probabilities of `T_(1)` winning, drawing and lossing a game against `T_(2)` are `1/6,1/6and 1/3,` respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams `T_(1) and T_(2)` respectively, after two games. `P(X=Y)` isA. `11/36`B. `1/3`C. `13/36`D. `1/2`
• A fair die is tossed repeatedly until a 6 is obtained. Let X denote the number of tosses required. The probability that `X=3` equalsA. `25//216`B. `25//36`C. `5//36`D. `125//216`
• Three numbers are chosen at random without replacement from `{1,2,3,...,8}.` The probability that their minimum is 3, given that maximum is 6, is:A. `3/8`B. `1/5`C. `1/4`D. `2/5`
• If C and D are two events such that `C subD`and P(D) is not equal to 0,` then the correct statement among the following isA. `P(C|D)=(P(D))/(P(D))`B. `P(C|D)=P(C)`C. `P(C|D)geP(C)`D. `P(C|D)ltP(C)`
• If A and B are two events such that `P(A)=0.6 and P(B)=0.8,` if the greatest value that `P(A//B)` can have is p, then the value of 8p is______.
• One ticket is selected at random from 50 ticketsnumbered 00, 01, 02, ... , 49. Then the probability that the sum of thedigits on the selected ticket is 8, given that the product of these digits iszero, equals(1) 1/14 (2) 1/7(3) 5/14(4) 1/50A. `1/14`B. `1/7`C. `5/14`D. `1/50`
• An urn contains 3 red balls and `n`white balls. Mr. A draws two balls together from the urn. Theprobability that they have the same color is 1/2 Mr. B. Draws one balls formthe urn, notes its color and replaces it. He then draws a second ball fromthe urn and finds that both balls have the same color is 5/8. The possiblevalue of `n`is`9`b. `6`c. `5`d. 1
• A box `B_(1)` contains 1 white ball, 3 red balls, and 2 black balls. An- other box `B_(2)` contains 2 white balls, 3 red balls and 4 black balls. A third box `B_(3)` contains 3 white balls, 4 red balls, and 5 black balls. If 2 balls are drawn (without replecement) from a randomly selected box and one of the balls is white and the other ball is red the probability that these 2 balls are drawn from box `B_(2)` isA. `116//182`B. `126//181`C. `65//181`D. `55//181`