## Book: Mathematics Part-II

### Chapter: 13. Probability

#### Subject: Maths - Class 12th

##### Q. No. 14 of Exercise 13.2

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14
##### Probability of solving specific problem independently by A and B are 1/2 and 1/3 respectively. If both try to solve the problem independently, find the probability that(i) the problem is solved (ii) exactly one of them solves the problem.

Given:

P(A) = Probability of solving the problem by A = 1/2

P(B) = Probability of solving the problem by B = 1/3

Because A and B both are independent.

P (A B) = P(A) . P(B)

P (A B) =

P(A) = 1 – P(A) = 1 – 1/2 = 1/2

P(B) = 1 – P(B) =

(i) the problem is solved

The problem is solved, i.e. it is either solved by A or it is solved by B.

= P(A B)

As we know, P (A B) = P(A) + P(B) - P (A B)

P (A B) =

(ii) exactly one of them solves the problem

i.e. either problem is solved by A but not by B or vice versa

i.e. P(A).P(B) + P(A).P(B)

=

=

P(A).P(B) + P(A).P(B) = 1/2

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