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On her​ birthday, a girl receives a giant box of​ crème filled chocolates from a secret admirer. She only likes the ones with fruit flavored fillings and​ won't eat the others. The box says that​ 25% of the chocolates have fruit fillings. If she keeps choosing chocolates and biting into​ them, how many should she expect to reject until finding the first fruit flavored​ one?

Respuesta :

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Answer:

4 chocolates

Step-by-step explanation:

Since the problem states that the girl received a "giant box", this situation can be treated as if there is replacement, since the change in the probability  of getting a chocolate with fruit filling would be minimal after picking a random chocolate.

Therefore, the expected number of choices she has to make before finding the first fruit flavored​ one is obtained by dividing 1 by the probability of a fruit flavored one:

[tex]E(X) =\frac{1}{P(X)}\\ E(X) = \frac{1}{0.25}=4[/tex]

She should expect to choose 4 chocolates.

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