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In a weekday, Jeremy will eat Panda Express 35% of the time and drink Starbucks 40% of the time. If given that he doesn't drink Starbucks, the probability he eats Panda Express is 0.5. Calculate the probability he will eat Panda Express and drink Starbucks at the same time.

Answer :

Therefore, the probability that Jeremy will eat Panda Express and drink Starbucks at the same time is 0.175 or 17.5%.

Let's calculate the probability that Jeremy will eat Panda Express and drink Starbucks at the same time.

Let's define the events:

A: Jeremy eats Panda Express

B: Jeremy drinks Starbucks

We are given:

P(A) = 0.35 (probability Jeremy eats Panda Express)

P(B) = 0.4 (probability Jeremy drinks Starbucks)

P(A|~B) = 0.5 (probability Jeremy eats Panda Express given he doesn't drink Starbucks)

To calculate the probability of Jeremy eating Panda Express and drinking Starbucks at the same time, we can use the formula for the intersection of two events:

P(A ∩ B) = P(A) * P(B|A)

However, we don't have direct information about P(B|A). But we can use the complement rule to find it:

P(A|~B) = 1 - P(~A|~B)

P(~A|~B) = 1 - P(A|~B)

Now, we can calculate P(B|A):

P(B|A) = 1 - P(~A|~B)

P(A ∩ B) = P(A) * P(B|A)

Let's substitute the values into the formulas:

P(B|A) = 1 - P(~A|~B) = 1 - P(A|~B) = 1 - 0.5 = 0.5

P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.5 = 0.175

Therefore, the probability that Jeremy will eat Panda Express and drink Starbucks at the same time is 0.175 or 17.5%.

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