3. In a class of 260 seniors, 93 study Spanish, 95 study Chemistry, 165 study Ma

Question

3. In a class of 260 seniors, 93 study Spanish, 95 study Chemistry, 165 study Mathematics, 18 study Spanish and Chemistry, 75 study Chemistry and Math, 20 study Math and Spanish and 15 study all three subjects. Suppose we choose one of the seniors at random. Use this information to answer the following questions. a) What is the probability that the chosen student doesn't study any of these subjects? b) What is the probability that the chosen student doesn't study Spanish, given that they study mathematics? c) What is the probability that the chosen student studies chemistry, given that they study mathematies or Spanish? d) What is the probability that the chosen student studies both mathematics and chemistry, given that they don't study Spanish?

Explanation / Answer

a) P(doesn't study any of the subject) = 1 - P(either of the subject)

                                                             = 1 - (93 + 95 + 165 - 18 - 75 - 20 + 15)/260

                                                             = 1 - 0.98 = 0.02

b) P(doesn't study spanish | study mathmatics) = P(doesn't study spanish and study mathmatics)/P( study mathmatics) = 75/165 = 0.45

c) P(study chemistry | study mathe matics or spanish) = 15/(165 + 18 - 20) = 0.09

d) P(both mathmatics and chemistry | doesn't spanish) = 75/(95 + 165 - 75) = 0.41

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