The probability of selecting 2 men and a woman is
The sample space is made up of 7 men and 5 women. So we have a total of 12 people.
If 3 applicants are randomly selected without replacement, there will be three mutually exclusive possibilities;
The final probability will have the form
because the possibilities are mutually exclusive.
<h3>Computing the Probability of each possibility</h3>Each mutually exclusive possibility is made up of dependent events. This is because when selection is done without replacement, it affects the size of the sample space.
- The Probability of selecting a Man, then a Man, then a Woman is
- The Probability of selecting a Man, then a Woman, then a Man is
- The Probability of selecting a Woman, then a Man, then a Man is
The final probability is
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