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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 17 Page P19

Practice makes perfect
a Let's add the row and column totals to the table.
Class Freshman Sophomore Junior Senior Total
Attended 48 90 224 254 616
Not attended 182 141 36 8 367
Total 230 231 260 262 983
From the bottom right entry we can see, there were 983 students in North Coast High School. If we divide the numbers with this total, we get the probabilities associated with the cells. Notice that 983 is a prime number, so the fractions cannot be reduced.
Class Freshman Sophomore Junior Senior Total
Attended 48/983 90/983 224/983 254/983 616/983
Not attended 182/983 141/983 36/983 8/983 367/983
Total 230/983 231/983 260/983 262/983 1

We are interested in the probability that a randomly selected student has not attended a game, given that he or she is a freshman. Let's use the Conditional Probability Formula to write this probability as the quotient of two unconditional probabilities. P(not attended | freshman)=P(not attended and freshman)/P(freshman) Let's use the color we used in the formula to highlight the relevant entries of the table.

Class Freshman Sophomore Junior Senior Total
Attended 48/983 90/983 224/983 254/983 616/983
Not attended 182/983 141/983 36/983 8/983 367/983
Total 230/983 231/983 260/983 262/983 1

If we substitute these values in the formula, we get the answer to the question. P(not attended | freshman)=182/983/230/983=91/115≈ 0.791 The probability that a randomly selected student has not attended a football game, given that he or she is a freshman, is 91115, or about 0.791.

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 an upperclassman, given that he or she has attended a game. We can again use the Conditional Probability Formula.
P(upperclassman | attended)=P(uperclassman and attended)/P(attended) Let's use the color we used in the formula to highlight the relevant entries of the table. Note that both juniors and seniors are upperclassman, so we need to consider both cells when we calculate the probability in the numerator.
Class Freshman Sophomore Junior Senior Total
Attended 48/983 90/983 224/983 254/983 616/983
Not attended 182/983 141/983 36/983 8/983 367/983
Total 230/983 231/983 260/983 262/983 1

Since there is no student who is both a junior and a senior, the probability of a student being an upperclassman who has attended a game is the sum of the corresponding junior and senior probabilities. 224/983+ 254/983=224+254/983= 478/983 If we substitute the values in the conditional Probability Formula, we get the answer to the question. P(upperclassman | attended)=478/983/616/983=239/308≈ 0.776 The probability that a randomly selected student is an upperclassman, given that he or she has attended a football game, is 239308, or about 0.776.

Subchapter links expand_more
arrow_right Exercises p.19-P19
1
Exercises 2 (Page P19)
3
4
5
Exercises 6 (Page P19)
7
8
Exercises 9 (Page P19)
Exercises 10 (Page P19)
11
Exercises 12 (Page P19)
13
14
Exercises 15 (Page P19)
Exercises 16 (Page P19)
Exercises 17 (Page P19)