A number x is selected at random in the interval 1 2 Let the

A number x is selected at random in the interval [-1, 2]. Let the events A = {x0.75}. Find the probabilities of A, B, B, and A C. Compute the probability of A B C.

Solution

We need to simplify B. before getting further.

B = {| x - 0.5 | < 0.5 }

thus, -1 < x < 1 is the range for B.

a) The probabilities would be division of the lengths.

L(S) = 3

L(A) = 1

L(B) = 2

L(C) = 1.25

P(A) = 1/3

P(B) = 2/3

P(A and B) = 1/3 (since common intersection of A and B is from -1 to 0)

P(A and C) = 0.25 /3 = 1 / 12 (since common intersection of A and C is from 0.75 to 1)

b)

P ( A or B or C) = 3 / 3 = 1

since the union of A, B and C covers the entire sample space

Hope this helps.