Question

Given P(A)=0.31P(A)=0.31, P(B)=0.5P(B)=0.5 and P(A\text{ or }B)=0.585P(A or B)=0.585, find the value of P(A\text{ and }B)P(A and B), rounding to the nearest thousandth, if necessary.

Answer 1

Answer: $P(A\text{ and B\rparen = 0.225 }$Explanation:

Given:

P(A) = 0.31

P(B) = 0.5

P(A or B) = 0.585

To find:

P(A and B)

To determine P(A and B), we will apply the formula:

$P(A\text{ or B\rparen}=\text{ P\lparen A\rparen + P\lparen B\rparen}-\text{ P\lparen A and B\rparen}$$\begin{gathered} substitute\text{ the values:} \\ 0.585\text{ = 0.31 + 0.5 +- P\lparen A and B\rparen} \\ 0.585\text{ = 0.81 - }P(A\text{ and B\rparen} \\ 0.585+\text{ P\lparen A and B\rparen = 0.81} \\ P(A\text{ and B\rparen = 0.81 - 0.585} \end{gathered}$$P(A\text{ and B\rparen = 0.225 }$