Search any question & find its solution
Question:
Answered & Verified by Expert
A salesman has a $70 \%$ chance to sell a product to any customer. The behaviour of successive customers is independent. If two customers $\mathrm{A}$ and $\mathrm{B}$ enter, what is the probability that the salesman will sell the product to customer A or B?
Options:
Solution:
1206 Upvotes
Verified Answer
The correct answer is:
$0.91$
$\quad P(A)=\frac{70}{100}=\frac{7}{10}=P(B)$
$A$ and $B$ are independent.
$\begin{aligned} \Rightarrow P(A \cap B) &=P(A) P(B) \\ \Rightarrow P(A \cup B) &=P(A)+P(B)-P(A \cap B) \\ &=\frac{7}{10}+\frac{7}{10}-\frac{7}{10} \times \frac{7}{10}=0.91 \end{aligned}$
$A$ and $B$ are independent.
$\begin{aligned} \Rightarrow P(A \cap B) &=P(A) P(B) \\ \Rightarrow P(A \cup B) &=P(A)+P(B)-P(A \cap B) \\ &=\frac{7}{10}+\frac{7}{10}-\frac{7}{10} \times \frac{7}{10}=0.91 \end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.