6. Multiplying Probabilities
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| Gender | Clubs | No Clubs | Total |
|---|---|---|---|
| Male | 156 | 242 | 398 |
| Female | 312 | 108 | 420 |
| Total | 468 | 350 | 818 |
The calculation of the other entries is similar. Let's write all the probabilities in fully simplified form.
| Gender | Clubs | No Clubs | Total |
|---|---|---|---|
| male | 78/409 | 121/409 | 199/409 |
| female | 156/409 | 54/409 | 210/409 |
| Total | 234/409 | 175/409 | 1 |
We are interested in the probability that a randomly selected student is a member of a club, given that he is male. Let's use the Conditional Probability Formula to write this probability as the quotient of two unconditional probabilities. P(club member | male)=P(club member and male)/P(male) Let's use the color we used in the formula to highlight the relevant entries of the table.
| Gender | Clubs | No Clubs | Total |
|---|---|---|---|
| Male | 78/409 | 121/409 | 199/409 |
| Female | 156/409 | 54/409 | 210/409 |
| Total | 234/409 | 175/409 | 1 |
If we substitute these values in the formula, we get the answer to the question. P(club member | male)=78/409/199/409=78/199≈ 0.392 The probability that a randomly selected student is a member of a club, given that he is male, is 78199, or about 0.392.
Let's use the color we used in the formula to highlight the relevant entries of the table.
| Gender | Clubs | No Clubs | Total |
|---|---|---|---|
| Male | 78/409 | 121/409 | 199/409 |
| Female | 156/409 | 54/409 | 210/409 |
| Total | 234/409 | 175/409 | 1 |
If we substitute these values in the formula, we get the answer to the question. P(not club member | female)=54/409/210/409=9/35≈ 0.257 The probability that a randomly selected student is not a club member, given that she is female, is 935, or about 0.257.
Let's use the color we used in the formula to highlight the relevant entries of the table.
| Gender | Clubs | No Clubs | Total |
|---|---|---|---|
| Male | 78/409 | 121/409 | 199/409 |
| Female | 156/409 | 54/409 | 210/409 |
| Total | 234/409 | 175/409 | 1 |
If we substitute these values in the formula, we get the answer to the question. P(male | not club member)=121/409/175/409=121/175≈ 0.691 The probability that a randomly selected student is a male, given that he is not a member of a club, is 121175, or about 0.691.