Question

X can solve 80% of the problems while Y can solve 90% of the problems given in a statistics book. A problem is selected at random.what is the probability that at least one of them will solve the same?​

Answer 1

Answer:

orrect option is

C

0.94

Probability that Ashmit and Amisha can solve

=0.8×0.7=0.56

Probability that Ashmit can solve and Amisha cannot solve

=0.8×0.3=0.24

Probability that Ashmit cannot solve and Amisha can solve

=0.2×0.7=0.14

Therefore, probability that at least one of them will solve

=0.56+0.24+0.14=0.94

Answer 2

Given: X can solve 80% of the problems

Y can solve 90% of the problems

To find: The probability that at least one of them will solve the randomly selected problem

Solution: Let the probability of X solving a problem be P(X) and the probability of Y solving a problem be P(Y).

Hence, P(X) = 0.80 and P(Y) = 0.90.

∴ P(X') = 1 - 0.80 = 0.20

P(Y') = 1 - 0.90 = 0.10

The event of X solving the problem is independent of the event of Y solving the problem.

Hence, the probability that at least one of them will solve the problem

= 1 - (P(X') × P(Y'))

= 1 - (0.20 × 0.10)

= 1 - 0.02

= 0.98