Question

The probability that it will rain tomorrow is

1/2. The probability that I will oversleep
tomorrow (which has nothing to do with rain)
is 1/4. What is the probability that I both
oversleep and it rains?

a. 1/8
b. 1/2
C. 3/4
d. 3/8
e. 1/6

Answer 1

To determine the probability that both events occur, we need to multiply their probabilities together, using the formula for the intersection of two independent events:

P(A and B) = P(A) × P(B)

Let A be the event "it rains tomorrow" and B be the event "I oversleep tomorrow". We are given:

P(A) = 1/2
P(B) = 1/4

So the probability that both events occur is:

P(A and B) = P(A) × P(B) = (1/2) × (1/4) = 1/8

Therefore, the answer is (a) 1/8.