Q. 195.0( 1 Vote )

Three persons A,

Answer :

Given: 3 persons A, B and C apply for a job of Manager in a Private Company


To find: the probability that due to the appointment of C no change take place


Formula used:


Bayes’ Theorem:


Given E1, E2, E3....,En is mutually exclusive and exhaustive events; we can find the conditional probability P(Ei|A) for any event A associated with Ei as follows:



Let A: Change does not occur


E1: selection of A


E2: selection of B


E3: selection of C


Chances of selection of A, B and C are in the ratio 1:2:4


Probability of selection of A = P(E1) =


Probability of selection of B = P(E2) =


Probability of selection of C = P(E3) =


Probability that A introduces change = 0.8


Probability that A does not introduce change = P(A|E1) = 1 – 0.8 = 0.2


Probability that B introduces change = 0.5


Probability that B does not introduce change = P(A|E2) = 1 – 0.5 = 0.5


Probability that C introduces change = 0.3


Probability that C does not introduce change = P(A|E3) = 1 – 0.3 = 0.7


The probability that due to the appointment of C, there is no change take place, P(E3|A)









Hence, the probability that due to the appointment of C no change take place is 0.7


OR


Given: A starts the game of throwing a pair of dice and alternatively by B. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10


To find: the probability that B wins


Total outcomes when 2 dice are thrown = 36


{ (1, 1); (1, 2); (1, 3) and so on}


Total favorable outcomes for A to get a total of 7 = 7


{(1, 6), (6, 1), (3, 4), (4, 3), (2, 5), (5, 2)}


Hence, Probability of A winning the game = P(A) =


The probability of A losing the game


Total favorable outcomes for B to get a total of 10 = 3


{(4, 6), (6, 4), (5, 5)}


Hence, Probability of B winning the game = P(B) =


The probability of B losing the game


Let X be A wins, Y be A loses, S be B wins, and F be B loses


As A starts the game, the game will stop when B wins


Possible sequence = {YS, YFYS, YFYFYS…………………}


YS denotes A loses then B wins


The probability of B winning in 2nd throw =


The probability of B winning in 4th throw =


This will form a G.P.



Sum of the term of a G.P. upto infinity is given by,



where a is the first term, and r is a common ratio




So,







Hence, the Probability that B wins is


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