Question

A salesman has a $70\%$ chance to sell a product to any customer. The behaviour of successive customers is independent. If two customers A and B enter, what is the probability that the salesman will sell the product to customer A or B?

• A. $0.98$
• B. $0.91$
• C. $0.70$
• D. $0.49$

Answer 1

The correct option is B $0.91$

Let $P\left(A\right)$ and $P\left(B\right)$ be the probability that salesman sells the product to costumer $A$ and $B$ respectively

$\therefore P\left(A\right)=P\left(B\right)=70\%=0.7$

Probability that the salesman will sell the product to customer $A$ or $B=P(A\cap \overline{B})+P(\overline{B}\cap A)+P(A\cap B)$

$=P\left(A\right)P\left(\overline{B}\right)+P\left(\overline{A}\right)P\left(B\right)+P\left(A\right)\left(B\right)$ ...( $P\left(A\right)$ and $P\left(B\right)$ are independent)

$=\left(0.7\right)(1-0.7)+(1-0.7)\left(0.7\right)+\left(0.7\right)\left(0.7\right)$

$=0.21+0.21+0.49$

$=0.91$

Answer is option (B).