1. ## Probability based question

Consider two independent events, A and B, where the P(A) is 0.45 and the probability that A does not occur or B occurs is 0.70. Determine the probability that event B occurs.

Any help is greatly appreciated

2. ## Re: Probability based question

Two independent events means that $P(A\text{ and }B) = P(A)P(B)$.

$$P(\text{not }A\text{ or }B) = P(\text{not }A)+P(B) - P(\text{not }A\text{ and }B) = (1-P(A))+P(B) - (1-P(A))P(B)$$

Plugging in the numbers you know:

$$0.7 = (1-0.45)+P(B)-(1-0.45)P(B)$$

$$0.15 = 0.45P(B)$$

$$P(B) = \dfrac{1}{3}$$