Question

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Jeffrey estimates there is 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 Jeffrey eating pizza, if he drinks cola?

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

Answer 1

d. 50%

Explanation:

To find the probability of Jeffrey eating pizza if he drinks cola, we can use conditional probability.

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

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

In this case:

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

The given probabilities for these events are:

• P(A) = 0.40
• P(B) = 0.60
• P(A and B) = 0.30

Substitute the probabilities into the conditional probability formula to determine the probability of Jeffrey eating pizza given he drinks cola:

`\sf P(A|B) = (0.3)/(0.6)`

`\sf P(A|B) = 0.5`

`\sf P(A|B) = 50\%`

So, the probability of Jeffrey eating pizza if he drinks cola is 50%.

Answer 2

d. 50%

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Use the formula for conditional probability:

• P(B|A) = P(A ∩ B) / P(A),

where P(A) is the probability of event A (drinking cola), P(B) is the probability of event B (eating pizza), and P(A ∩ B) is the probability of both events happening together.

In this case,

• P(A) is the probability of drinking cola which is 0.60,
• P(B) is the probability of eating pizza which is 0.40,
• P(A ∩ B) is the probability of eating pizza and drinking cola which is 0.30.

So if we apply these values to the formula, we get:

• P(B|A) = P(A ∩ B) / P(A) = 0.30 / 0.60 = 0.50 (which is Option D)

So, if Jeffrey drinks cola, the probability of him also eating pizza is 50%.