Probability topic

Question

if R and E are independent events then P(R∩E)=0.36 then which of the following could be Probability R

 

(a)0.3

(b)0.35

(c)0.4

(d)0.6

(e)0.9

Answer 1

There are two things to know, to solve this problem:

 

1. When two events are independent, the probability of both happening is the product of the individual probabilities of each event.

2. The probability of any event can never be more than 1.

 

So P(R∩E)=0.36 means the following:

 

P(R) * P(E) = 0.36

P(E) <= 1.0

 

You can look at these as a system that can be solved.  You can divide an equation by an inequality as long as you reverse the direction of the inequality in the result.

 

P(R) * P(E) / P(E) >= 0.36 / 1.0

P(R) >= 0.36

 

So P(R) can be c, d, or e.