Question

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Jefferey estimates that there's a 40% chance he'll eat pizza for dinner, a 60% chance he'll drink cola, and a 30% he'll eat pizza and drink cola. What's the probability of Jefferey drinking cola, if he eats pizza?

a. 50%
b. 24%
c. 13.33%
d. 75%

Answer 1

d. 75%

Explanation:

To determine the probability of Jefferey drinking cola given that he eats pizza, we can use conditional probability.

In this case:

• Let P be the event that he eats pizza.
• Let C be the event that he drinks cola.

The given probabilities are:

• P(P) = 0.4 (probability of Jefferey eating pizza)
• P(C) = 0.6 (probability of Jefferey drinking cola)
• P(P ∩ C) = 0.3 (probability of a Jefferey eating pizza and drinking cola)

The probability of a Jefferey drinking cola given that he eats pizza, denoted as P(C | P), can be calculated using the formula for conditional probability:

`\boxed{\begin{array}{c}\underline{\sf Conditional\;Probability\;}\\\\\sf P(C|P)=(P(P \cap C))/(P(P))\end{array}}`

Substitute the given probabilities:

`\sf P(C|P)=(0.30)/(0.40)=0.75=75\%`

Therefore, the probability of Jefferey drinking cola, given that he eats pizza, is 75%.