Keisha and Kelly have an astronomy club devoted to observing the moon. If the moon is visible 28 out of 29 days and the girls can make it outside 14 days per 29 days, what is the probability they will go out on a night when the moon is not visible?
p(outside) = 14/29
p(not visible) = 1/29
probability of two independent events is the product of the individual probabilities
Thanks again Scott!
To find the probability that the girls will go out on a night when the moon is not visible, we need to determine the probability of two independent events happening concurrently:
1. The moon is not visible on a given night.
2. The girls choose to go out on that night.
Let's break it down step by step:
Step 1: Find the probability that the moon is visible on any given night.
The moon is visible 28 out of 29 days, so the probability of the moon being visible on any given night is 28/29.
Step 2: Find the probability that the moon is not visible on any given night.
The complement of an event is the opposite of that event. So, the probability of the moon not being visible on any given night is 1 - (28/29) = 1/29.
Step 3: Find the probability that the girls choose to go out on any given night.
The girls can make it outside 14 days out of 29, so the probability of them choosing to go out on any given night is 14/29.
Step 4: Find the probability that both events occur concurrently.
To find the probability of two independent events happening at the same time, you multiply their individual probabilities. So, the probability that the moon is not visible on a given night and the girls choose to go out is (1/29) * (14/29) = 14/841.
Therefore, the probability that the girls will go out on a night when the moon is not visible is 14/841.