Exactly half of the students in a class of 36 students love milk chocolate, exac

Question

Exactly half of the students in a class of 36 students love milk chocolate, exactly 1/3 of the them love dark
chocolate, and exactly 1/6 of the them fall into both categories.

You pick a student at random.

Let M denote the event that the randomly selected student is a milk chocolate lover.
Let D denote the event that the randomly selected student is a dark chocolate lover.

(a) The randomly selected student reveals that she is a milk chocolate lover. Compute the probability that the student is also a dark chocolate lover.
(b) Are events M and D independent? Why? Prove your claim.

Question 1. Chocolate lovers, again. Exactly half of the students in a class of 36 students love milk chocolate, exactly 1/3 of the them love dark chocolate, and exactly 1/6 of the them fall into both categories. You pick a student at random. Let M denote the event that the randomly selected student is a milk . Let D denote the event that the randomly selected student is a dark (a) The randornlykoled student reveals that she is a milk chocolate chocolate lover chocolate lover lover. Compute the probability that the student is also a dark chocolate lover. (b) Are events M and D independent? Why? Prove your claim.

Explanation / Answer

here P(M) =1/2 ; P(D) =1/3 ; P(M n D) =1/6

a) probability that the student is also a dark chocolate lover given  milk chocolate lover

=P(D|M) =P(D nM)/P(M) =(1/6)/(1/2 )=1/3

b) as P(Mn D) =P(M)*P(D)

therefore M and D are independent.

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