Question

2. Exclude leap years from the following calculations. What is the probability that a randomly chosen person has a birthday on the 15th of any month or in March? a) State the sample space and its size.

b) State the two events and their respective sizes.

c) Are the two events from part b) disjoint? If so, why? If not, what is the intersection and what is its size?

d) Now, find the probability that was originally asked.

Answer 1

A) Sample space = { 15jan, 15feb, 15april, 15may, 15june, 15july, 15august, 15september, 15october, 15november, 15december, all dates of march}

Sample size = 42

B) Two events are A= {15jan, 15feb, 15march, 15april, 15may, 15june,15july,15august,15september,15october, 15november, 15december}

Sample size A= 12

B={1,2,3..........31 march}

Sample size = 31

C) A and B are not disjoint since there is common element in A and B.

Intersection A and B = {15march} and size =1

D) P(A U B) = P(A) + P(B) - P(A and B)

= 12/365 + 31/365 - 1/365

=42/365