Question

P(a) = 1 2 p(b) = 1 5 p(c) = 1 8 find the probability. (enter the probability as a fraction.) p[(a ∪ b) ∩ c]

Answer 1

To find the probability P[(a ∪ b) ∩ c], you need to multiply the probability of (a ∪ b) by the probability of c. However, the probability of (a ∩ b) is not provided, so the exact probability cannot be calculated.

Step-by-step explanation:

To find the probability of the intersection of two events, you need to multiply their individual probabilities. In this case, you want to find the probability of the intersection of events (a ∪ b) and c. The probability of a ∪ b is the sum of the probabilities of a and b minus the probability of their intersection, which is P(a) + P(b) - P(a ∩ b). Multiplying this probability by P(c) will give you the desired probability.

Let's calculate it:

P(a ∪ b) = P(a) + P(b) - P(a ∩ b) = 1/2 + 1/5 - P(a ∩ b)

P(a ∪ b) ∩ c = (1/2 + 1/5 - P(a ∩ b)) × 1/8

Now, we need to find the value of P(a ∩ b). Unfortunately, the information provided does not define the probability of the intersection of events a and b, so we cannot calculate the exact probability.