7 Exercise 7 In a certain college, 25% of the students failed mathematics, 15% f

Question

7 Exercise 7 In a certain college, 25% of the students failed mathematics, 15% failed chemistry and 10% failed both mathematics and chemistry. A student is selected at random. a) Define the two relevant events. b) If the student failed chemistry, what is the probability that he failed mathematics? c) If the student failed mathematics, what is the probability that he failed chemistry? d) What is the probability that the student failed mathematics or chemistry e) What is the probability that the student failed neither mathematics nor chemistry?

Explanation / Answer

a) two relevent events are student failing mathematics which can be denoted as M and student failing Chemistry as C

here P(M)=0.25 and P(C)=0.15 ; P(M and C)=0.10

b) probability=P(M|C)= P(M and C)/P(C)=0.10/0.15=0.6667

c) probability=P(C|M)= P(M and C)/P(M)=0.1/0.25=0.40

d) probability=P(M UC) =P(M)+P(C)-P(M and C)=0.25+0.15-0.10=0.30

e) probability =1-P(MUC) =1-0.3 =0.70

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