Question

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Jeffrey estimates that there's a 40% chance he'll eat pizza for dinner. If he eats pizza, there's an 80 % chance he'll drink cola. What's the probability of Jeffrey eating pizza and drinking cola?

a. 32%
b. 20%
c. 16%
d. 40%

Answer 1

a. 32%

Explanation:

To find the probability of Jeffrey eating pizza and drinking cola, we can use conditional probability.

The conditional probability of an event B occurring given that event A has occurred is denoted as P(B | A) and is calculated using the formula:

`\sf P(B|A) = (P(A\; and \;B))/(P(A))`

In this case:

• Event A is eating pizza.
• Event B is drinking cola.

The given probabilities for these events are:

• Probability of Jeffrey eating pizza: P(A) = 0.40
• Probability of Jeffrey drinking cola given he eats pizza: P(B | A) = 0.8
• Probability of Jeffrey eating pizza and drinking cola: P(A and B)

Substitute the probabilities into the conditional probability formula to determine the probability of Jeffrey eating pizza and drinking cola, P(A and B):

`\sf 0.8 = (P(A\; and \;B))/(0.4)`

`\sf 0.8\cdot 0.4 = (P(A\; and \;B))/(0.4)\cdot 0.4`

`\sf P(A\; and \;B)=0.32`

`\sf P(A\; and \;B)=32\%`

So, the probability of Jeffrey eating pizza and drinking cola is 32%.

Answer 2

a. 32%

===================

Multiply the probability of Jeffrey eating pizza (40%) by the probability of him drinking cola given that he eats pizza (80%).

• Probability of eating pizza and drinking cola = (40% * 80%) = 0.4 * 0.8 = 0.32 = 32%

Therefore, the probability of Jeffrey eating pizza and drinking cola is 32% (option a).