McGraw Hill Glencoe Algebra 2, 2012
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McGraw Hill Glencoe Algebra 2, 2012 View details
6. Multiplying Probabilities
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Exercise 16 Page P19

a First, let's add the row and column totals to the table.
Gender Clubs No Clubs Total
Male
Female
Total
From the bottom right entry, we can see that there were students in King High School. If we divide the numbers with this total, we will get the probabilities associated with the cells. Let's see the probability that a randomly selected student is a male club member.
The calculation of the other entries is similar. Let's write all the probabilities in fully simplified form.
Gender Clubs No Clubs Total
male
female
Total
We are interested in the probability that a randomly selected student is a member of a club, he is male. Let's use the Conditional Probability Formula to write this probability as the quotient of two unconditional probabilities.
Let's use the color we used in the formula to highlight the relevant entries of the table.
Gender Clubs No Clubs Total
Male
Female
Total
If we substitute these values in the formula, we get the answer to the question.
The probability that a randomly selected student is a member of a club, given that he is male, is or about
b To answer the question in part B, we can use the same table of probabilities. We are interested in the probability that a randomly selected student is not a club member, she is female. We can again use the Conditional Probability Formula.
Let's use the color we used in the formula to highlight the relevant entries of the table.
Gender Clubs No Clubs Total
Male
Female
Total
If we substitute these values in the formula, we get the answer to the question.
The probability that a randomly selected student is not a club member, given that she is female, is or about
c To answer the question in part C, we yet again use the same table of probabilities. We are interested in the probability that a randomly selected student is male, he is not a member of a club. The Conditional Probability Formula is again useful.
Let's use the color we used in the formula to highlight the relevant entries of the table.
Gender Clubs No Clubs Total
Male
Female
Total
If we substitute these values in the formula, we get the answer to the question.
The probability that a randomly selected student is a male, given that he is not a member of a club, is or about