There are 28 people in a meeting. The probability that a person chosen at random is a man is one-half. Calculate the number of women in the meeting.
In this question, we are asked to calculate the number of women in a meeting, given
that the probability that a man is chosen is one-half. We are told that the total number of people in the meeting is 28. We recall that the probability of an event can be written as a fraction, where the
numerator is the number of successful outcomes and the denominator is the total
number of outcomes. This holds provided that every item is equally likely to be selected.
The probability of selecting a man is one-half, so if there are 𝑚 men, we know that
one-half is equal to 𝑚 over 28. Rearranging this equation, we see that the number of men is equal to one-half of 28,
which is equal to 14. We can therefore calculate the number of women in the meeting by subtracting 14 from
28, which is equal to 14. We can therefore conclude that the number of women in the meeting is 14.