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59 . Write the symbols for the probability that the student is an education major, given that the student is male.
60 . Events
A and
B are independent.
If
P (
A ) = 0.3 and
P (
B ) = 0.5, find
P (
A AND
B ).
61 .
C and
D are mutually exclusive events.
If
P (
C ) = 0.18 and
P (
D ) = 0.03, find
P (
C OR
D ).
62 . In a high school graduating class of 300, 200 students are going to college, 40 are planning to work full-time, and 80 are taking a gap year. Are these events mutually exclusive?
Use the following information to answer the next two exercises. An archer hits the center of the target (the bullseye) 70 percent of the time. However, she is a streak shooter, and if she hits the center on one shot, her probability of hitting it on the shot immediately following is 0.85. Written in probability notation:
P (
A ) =
P (
B ) =
P (hitting the center on one shot) = 0.70
P (
B |
A ) = P(hitting the center on a second shot, given that she hit it on the first) = 0.85
63 . Calculate the probability that she will hit the center of the target on two consecutive shots.
64 . Are P ( A ) and P ( B ) independent in this example?
Use the following information to answer the next three exercises. The following contingency table displays the number of students who report studying at least 15 hours per week, and how many made the honor roll in the past semester.
Honor roll | No honor roll | Total | |
---|---|---|---|
Study at least 15 hours/week | 200 | ||
Study less than 15 hours/week | 125 | 193 | |
Total | 1,000 |
65 . Complete the table.
66 . Find P (honor roll|study at least 15 hours per week).
67 . What is the probability a student studies less than 15 hours per week?
68 . Are the events “study at least 15 hours per week” and “makes the honor roll” independent? Justify your answer numerically.
69 . At a high school, some students play on the tennis team, some play on the soccer team, but neither plays both tennis and soccer. Draw a Venn diagram illustrating this.
70 . At a high school, some students play tennis, some play soccer, and some play both. Draw a Venn diagram illustrating this.
1 .
2 . c
3 . d
4 . d
5 . c
6 . Answers will vary.
Sample Answer: Any solution in which you use data from the entire population is acceptable. For instance, a professor might calculate the average exam score for her class: because the scores of all members of the class were used in the calculation, the average is a parameter.
7 . b
8 . a
9 .
# of years | Frequency | Relative Frequency | Cumulative Relative Frequency |
---|---|---|---|
<5 | 25 | 0.25 | 0.25 |
5–10 | 30 | 0.30 | 0.55 |
>10 | 45 | 0.45 | 1.00 |
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