determine whether the following individual events are overlapping or non-overlapping. then find the probability of the combined event.
randomly choosing a black sock or a small sock from a drawer in which an eighth of the socks are black and seven eighths are red and half of each color are small and half are large
To determine whether the events are overlapping or non-overlapping, we need to see if they can occur at the same time or not.
Event 1: Randomly choosing a black sock.
Event 2: Randomly choosing a small sock.
Since the sock can be both black and small, it means that these events are overlapping because we can choose a sock that is both black and small.
The probability of randomly choosing a black sock is 1/8 because there is 1 out of 8 socks that are black.
The probability of randomly choosing a small sock is 1/2 because half of each color (black and red) are small.
To find the probability of the combined event, we multiply the probabilities of the individual events:
Probability of choosing a black and small sock = Probability of choosing a black sock * Probability of choosing a small sock
= 1/8 * 1/2
= 1/16
Therefore, the probability of the combined event is 1/16.