A salesman is known to sell a product in 3 out of 5 attempts While another salesman in 2 out - Maths - Probability

Question

A salesman is known to sell a product in 3 out of 5 attempts
While another salesman in 2 out of 5 attempts Find the probability
that
(a) no sales will happen
(b)either of them will succeed in selling the product

Chetna Khanna · Accepted Answer

Let A be the event that the first salesman will sell the product and B be the event that the second salesman will sell the product.

Given $P (A) = \frac{3}{5}, P (B) = \frac{2}{5}$

(1) Probability that no sales will happen = P(A') × P(B')

$= (1 - P (A)) \times (1 - P (B)) = (1 - \frac{3}{5}) \times (1 - \frac{2}{5}) = \frac{2}{5} \times \frac{3}{5} = \frac{6}{25}$

(2) Probability that either of the salesman will succeed in selling the product = P(A') × P(B) + P(A) × P(B')

$= (1 - P (A)) \times P (B) + P (A) \times (1 - P (B)) = (1 - \frac{3}{5}) \times \frac{2}{5} + \frac{3}{5} \times (1 - \frac{2}{5}) = \frac{2}{5} \times \frac{2}{5} + \frac{3}{5} \times \frac{3}{5} = \frac{4}{25} + \frac{9}{25} = \frac{13}{25}$

-3

A salesman is known to sell a product in 3 out of 5 attempts.While another salesman in 2 out of 5 attempts.Find the probability that (a) no sales will happen (b)either of them will succeed in selling the product.

A salesman is known to sell a product in 3 out of 5 attempts.While another salesman in 2 out of 5 attempts.Find the probability that

(a) no sales will happen

(b)either of them will succeed in selling the product.