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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