A family has three children. Each child is a girl or a boy. Which of the followi

Question

A family has three children. Each child is a girl or a boy. Which of the following pairs of events are mutually exclusive or disjoint? a. The event that the oldest child is a girl and the event that the second and third children are boys. b. The event that the oldest child is a girl and the event that the oldest child is a boy. c. The event that at most one child is a girl and the event that the oldest child is a girl. d. The event that the oldest child is a boy and the event that all children are boys.

Explanation / Answer

Answer

(b) The event that the oldest child is a girl and the event that the oldest child is a boy.

Explanation Two events are called mutually exclusive or disjoint events if they can not occur at the same time. The probability of two mutually exclusive events occuring at the same time is 0.

So here, when the oldest child is a girl, it can not be a boy or if the oldest child is a boy, it can not be a girl. So these two events can not occur at the same time.

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