5. In a high school, 60% of the students live east of the school and 40% live west of the school. Among the students who live east of the school, 30% are in the math club, and among the students who live west of the school, 20% are in the math club. a. Find the probability that a randomly selected student is from east of the school and in the math club. b. Given that a student is from west of the school, what is the probability that he or she is in the math club? c. Is participation in the math club independent from whether a student lives east or west of the school? Justify your answer.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

a. Find the probability that a randomly selected student is from east of the school and in the math club:

P(east ∩ math club) = 0.6×0.3 = 0.18

b. Given that a student is from west of the school, what is the probability that he or she is in the math club?

P(west ∩ math club) = 0.4×0.2 = 0.08

c. Is participation in the math club independent of whether a student lives east or west of the school?

P(math club) = P(east ∩ math club) + P(west ∩ math club)

= 0.18 + 0.08

= 0.26

Thus, the probability for part (a) is 0.18, for part (b) is 0.08, and for part (c) is 0.26.

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