Probability Question 10

Events $D$ and $E$ are independent, with $P(D)=0.6$ and $P(D \text{ and } E)=0.18$ . Which of the following is true?

P(E) = 0.12

P(E)=0.4

P(D \text{ or } E)=0.28

P(D \text{ or } E)=0.72

Approach

We first attempt to find the probability of event $E$ .

P(D\cap E) = P(D)\cdot P(E)

0.18 = 0.6 \cdot P(E)

P(E)=0.3

We can not find the probability of $D$ or $E$ occuring:

P(D\cup E)=P(D) + P(E) - P(D\cap E)

P(D\cup E)= 0.6 + 0.3 - 0.18 =\boxed{0.72}