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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
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B
0.91
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C
0.70
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D
0.49
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Solution

The correct option is B $$0.91$$
Let $$P(A)$$ and $$P(B)$$ be the probability that salesman sells the product to costumer $$A$$ and $$B$$ respectively
$$\therefore P(A)=P(B)=70\%=0.7$$

Probability that the salesman will sell the product to customer $$A$$ or $$B=P(A\cap \overline{B})+P(\overline{B}\cap A )+P(A\cap B)$$
$$=P(A)P(\overline{B})+P(\overline{A})P(B)+P(A)(B)$$   ...( $$P(A)$$ and $$P(B)$$ are independent)
$$=(0.7)(1-0.7)+(1-0.7)(0.7)+(0.7)(0.7)$$
$$=0.21+0.21+0.49$$
$$=0.91$$
Answer is option (B).

Mathematics

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