Question

The weather forecast for the day shows a 45% chance of

rain, a 45% chance of lightning, and a 25% chance of lightning
and rain. Which statement is correct?
A. The chance of rain and the chance of lightning are
independent because .2025 = .25
B. The chance of rain and the chance of lightning are
independent events because .45 = .45
C. The chance of rain and the change of lightning are
dependent events because .2025 2.25
D. The chance of rain and the chance of lightning are
dependent events because .45 = .45

Answer 1

C

Explanation:

If two events are independent, the probability of both happening are:

P(A and B) = P(A) × P(B)

In this case, if rain and lightening were independent:

P(rain and lightening) = P(rain) × P(lightening)

P(rain and lightening) = 0.45 × 0.45

P(rain and lightening) = 0.2025

However, we're told that P(rain and lightening) is 0.25, not 0.2025.

Since 0.2025 ≠ 0.25, the events are not independent, so they are dependent.