Determine whether the following individual events are overlapping or non-overlapping. Then find the probability of the combined event.
Randomly choosing a white sock or a small sock from a drawer in which a third of the socks are white and two thirds are red and a fifth of each color are small and
four fifths are large
The individual events in this scenario are:
Event A: randomly choosing a white sock
Event B: randomly choosing a small sock
To determine if these events are overlapping or non-overlapping, we need to consider whether it is possible for both events A and B to occur simultaneously.
Event A: randomly choosing a white sock has a probability of 1/3, since a third of the socks are white.
Event B: randomly choosing a small sock has a probability of 1/5, since a fifth of each color (white and red) are small.
Since it is possible for a white sock to be small, it is possible for both events A and B to occur simultaneously. Therefore, the events are overlapping.
To find the probability of the combined event (both events A and B occurring), we multiply the probability of event A (1/3) by the probability of event B (1/5):
P(A and B) = P(A) * P(B) = (1/3) * (1/5) = 1/15
Therefore, the probability of the combined event (randomly choosing a white small sock) is 1/15.