Question

Q and r are not mutually exclusive events. if p(q) = 0.12, p(r) = 0.25, and p(q and r) = 0.03, find p(q or r).

Answer 1

0.34

Explanation:

The probability of A or B occurring if they are not mutually exclusive is given by

P(A)+P(B)-P(A and B)

In this case, we have

P(q)+P(r)-P(q and r)

= 0.12+0.25-0.03 = 0.34

Answer 2

So we are given the probabilities of q and r:

p (q) = 0.12

p (r) = 0.25

p (q and r) = 0.03

Actually to find for p (q or r), this simply means to add all the values of p (q). p (r) and p (q and r). If we are to draw a bubble diagram, the p (q and r) is the bubble intersection p (q) and p (r). We know that the word “OR” takes up all in the bubble diagram. Therefore:

p (q or r) = p (q) + p (r) + p (q and r)

Substituting the given values into the equation:

p (q or r) = 0.12 + 0.25 + 0.03

p (q or r) = 0.40