Question

The chance that A can solve a certain problem 1/4 , the chance that B can solved it is 2/3, then the chance that the problem will be solved if they both try is (a) 3/2
(b)1/3
(c) 1/4
(d) 3/4​

Answer 1

Answer:

orrect option is

B

0.66,0.50

Probability of solving the problem by A, P(A)=

2

1

Probability of solving the problem by B, P(B)=

3

1

Since the problem is solved independently by A and B,

∴P(AB)=P(A)⋅P(B)=

2

1

×

3

1

=

6

1

P(A′)=1−P(A)=1−

2

1

=

2

1

P(B′)=1−P(B)=1−

3

1

=

3

2

(i) Probability that the problem is solved =P(A∪B)

=P(A)+P(B)−P(AB)

=

2

1

+

3

1

−

6

1

=

6

4

=

3

2

=0.66

(ii) Probability that exactly one of them solves the problem is given by,

P(A)⋅P(B′)+P(B)⋅P(A′)

=

2

1

×

3

2

+

2

1

×

3

1

=

3

1

+

6

1

=

2

1

=0.50