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There is a 0.23 probability that a typical convenience store customer buys gasoline. The probability that a customer buys groceries is 0.76 and the conditional probability of buying groceries given that the customer buys gasoline is 0.85.

a) Find the probability that a typical customer buys both gasoline and groceries.

Respuesta :

Answer:

The probability that a typical customer buys both gasoline and groceries, P(Ga n Gr) = 0.1955

Step-by-step explanation:

Let the probability that a customer guys groceries be represented by P(Gr) and that of buying gasoline be P(Ga)

Given

P(Gr) = 0.76

P(Ga) = 0.23

P(Gr|Ga) = 0.85

For mutually exclusive events,

P(B|A) = (P(B n A))/P(A)

P(Gr|Ga) = (P(Gr n Ga))/P(Ga)

P(Gr n Ga) = P(Gr|Ga) × P(Ga)

P(Gr n Ga) = 0.85 × 0.23 = 0.1955

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