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There are 1000 students in a high school. Among the 1000 students, 150 students

ID: 3061659 • Letter: T

Question

There are 1000 students in a high school. Among the 1000 students, 150 students take AP Statistics, and 300 students take AP French. 100 students take both AP courses.

Let S be the event that a randomly selected student takes AP Statistics, and F be the event that a randomly selected student takes AP French.

Complete the Venn diagram by inserting the appropriate probabilities in each of its sections. If you prefer, you can make a Contingency Table instead of the Venn diagram.


b)         What is the probability of the event of (S or F)?

                                                                                                                                                                                                                                                                                    __________

c)         What is the probability of the event (S and not F)

                                                                                                                                                                                                                                                                              __________

d)         What is the probability of the event [neither (S nor F)]

                                                                                                                                                                                                                                                                              __________

Note:   (S or F) means: student takes AP Statistics or students take AP French.

            (S and not F) means: student takes AP Statistics and does not take AP French.

Explanation / Answer

a)

            F                  F'

S        100              50

S'        200             650

b) P(S or F) = P(S) + P(F - P(S and F) = 150/1000 + 300/1000 - 100/1000 = 0.35

c) P(S and not F) = P(S) - P(S and F) = 150/1000 - 100/1000 = 0.05

d) P(neither S nor F) = 1 - P(S or F) = 1 - 0.35 = 0.65