Question

6. E1 and E2 are events from the same sample space; P(E1)=0.37, P(E2)=0.45, and P(E1, E2)=0.14. a. Find the probability that E2 does not occur. b. Find the probability that either E1 or E2 occurs. c. Find the probability that neither E1 nor E2 occurs.

Answer 1

a. 0.55

b. 0.68

c. 0.18

Explanation:

a. The probability that E2 does not occur is one minus the probability that E2 occurs:

`1-P(E2)= 1- 0.45\\1-P(E2) = 0.55`

b. The probability that either E1 or E2 occurs is given by the sum of their individual probabilities minus their joint probability:

`P(E1\ or\ E2) = P(E1)+P(E2)-P(E1, E2)\\P(E1\ or\ E2)=0.37+0.45-0.14\\P(E1\ or\ E2)=0.68`

c. The probability that neither E1 nor E2 occurs is one minus the probability of E1 occurring minus the probability of E2 occurring:

`1-P(E1)-P(E2)= 1- 0.37 -0.45\\1-P(E1)-P(E2) = 0.18`