## Related questions with answers

Raaj works at the customer service call center of a major credit card bank. Cardholders call for a variety of reasons, but regardless of their reason for calling, if they hold a platinum card, Raaj is instructed to offer them a double-miles promotion. About 10% of all cardholders hold platinum cards, and about 50% of those will take the double-miles promotion. On average, how many calls will Raaj have to take before finding the first cardholder to take the doublemiles promotion?

Solution

VerifiedFor the number of calls before finding the first cardholder to take the double-miles promotion: The probability of success is;

$\begin{aligned} P &= (10\%)(50\%) \\ &= (0.10)(0.50) \\ &= 0.05 \\ \end{aligned}$

For the expected value;

$\begin{aligned} E(X) &= \mu = \dfrac{1}{p} \\ &= \dfrac{1}{0.05} \\ &= \boxed{20 \text{ calls}} \end{aligned}$

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