Question

It is known that 50% of all customers order a burger and 70% of all customers order fries at a certain diner. There is also a 85% chance that somebody who has ordered a burger will also order fries. Let events B = burger and F = fries for a randomly-selected customer. Enter decimal answers rounded to 4 decimal places.

Find P(B and F)
Find P(B or F)

Answer 1

To find the probabilities P(B and F) and P(B or F), you can use the probabilities provided and the concept of conditional probability.

1. P(B and F) (The probability that a customer orders both a burger and fries)

This can be calculated using the conditional probability formula:

P(B and F) = P(B) * P(F|B)

• P(B) is the probability of ordering a burger, which is 50% or 0.50.
• P(F|B) is the conditional probability of ordering fries given that the customer has ordered a burger, which is 85% or 0.85.

P(B and F) = 0.50 * 0.85 = 0.4250

So, P(B and F) is 0.4250 (rounded to 4 decimal places).

2. P(B or F) (The probability that a customer orders either a burger or fries or both)

To find P(B or F), you can use the inclusion-exclusion principle:

P(B or F) = P(B) + P(F) - P(B and F)

• P(B) is the probability of ordering a burger, which is 50% or 0.50.
• P(F) is the probability of ordering fries, which is 70% or 0.70.
• We already calculated P(B and F) as 0.4250 in the previous step.

P(B or F) = 0.50 + 0.70 - 0.4250 = 0.7750

So, P(B or F) is 0.7750 (rounded to 4 decimal places).