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At a certain college, 30% of the students major in engineering, 20% play club sports, and 10% both major in engineering and play club sports. A student is selected at random.
a) What is the probability that the student is majoring in engineering?
b) What is the probability that the student plays club sports?
c) Given that the student is majoring in engineering, what is the probability that the
student plays club sports?
d) Given that the student plays club sports, what is the probability that the student is
majoring in engineering?
e) Given that the student is majoring in engineering, what is the probability that the
student does not play club sports?
f) Given that the student plays club sports, what is the probability that the student is not
majoring in engineering?
Answer and Explanation
The venn diagram for the question is in the attachment.
Percentage majoring in engineering = 30% = 0.3
Percentage that plays club sport = 20% = 0.2
Percentage that major in engineering and play sport = 10% = 0.1
Percentage majoring in engineering & do not play club sport = 30 - 10 = 20% = 0.2
Percentage that plays club sport & do not major in engineering = 20 - 10 = 10% = 0.1
Total percentage = 100%
a) probability that student is majoring in Engineering P(E) = 30/100 = 0.3
b) probability that student plays club sport = 20/100 P(S) = 0.2
c) probability that the
student plays club sport given that the student is majoring in engineering, P(S|E) = (P(E and S))/(P(E))
P(E and S) = 10/100 = 0.1, P(E) = 0.3
P(S|E) = 0.1/0.3 = 0.3333
d) probability that the
student is majoring in engineering given that the student plays club sport, P(E|S) = (P(S and E))/(P(S))
P(S and E) = 10/100 = 0.1, P(S) = 0.2
P(E|S) = 0.1/0.2 = 0.5
e) probability that the
student does not play club sport given that the student is majoring in engineering, P(S'|E) = (P(E and S'))/(P(E))
P(E and S') = 20/100 = 0.2, P(E) = 0.3
P(S'|E) = 0.2/0.3 = 0.667
f) probability that the
student is not majoring in engineering given that the student plays club sport, P(E'|S) = (P(S and E'))/(P(S))
P(S and E') = 10/100 = 0.1, P(S) = 0.2
P(E|S) = 0.1/0.2 = 0.5
