Question

P(not A) = 0.6 and P(B) = 0.5 and events A and B are independent. what is the P(A and B)?

Answer 1

To determine the probability of independent P(A and B):

P(not A) = 0.6

`\begin{gathered} P(A)\text{ = 1 - P(not A)} \\ P(A)=1-0.6 \\ P(A)=0.4 \end{gathered}`
`P(B)=0.5`

As they are independent, product of their probabilities is the probability of occurring of both events simultaneously i.e.

P(A and B)=P(A)*P(B)

`\begin{gathered} P(A\text{ and B)=P(A) X P(B)} \\ P(A\text{ and B)= 0.4 x 0.5} \\ P(A\text{ and B)= 0.2} \end{gathered}`

Therefore the probability of event A and B : P(A and B) = 0.2