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(i) Two events E and F are such that P(E) = 0.6, P(F) = 0.2 and P(E∪F) 0.68. Are E and F independent? 

(ii) A die is thrown 6 times. If getting an odd number is a success, what is the probability of getting 

(a) 5 successes?

(b) At least 5 successes? 

(c) At most 5 successes?

1 Answer

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Best answer

(i) P(E∪F) = P(E) + P(F) – P(E∩F)

= 0.68 = 0.6 + 0.2 – P(E∩F) 

= P(E∩F)=O.12 P(E) x P(F)

= 0.2 x 0.6 = 0.12 = P(E∩F) 

Hence E and F are independent events. (ii) (a) Let X denotes the random variable of number of odd number in the throw of a die 6 times. Clearly X has a Binomial Distribution with n =6 and \(p=\frac{3}{6}=\frac{1}{2}\) 

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