Question

Given P(A)=0.5P(A)=0.5, P(B)=0.25P(B)=0.25 and P(A\text{ and }B)=0.185P(A and B)=0.185, find the value of P(A\text{ or }B)P(A or B), rounding to the nearest thousandth, if necessary.

Answer 1

We know the probabilities:

$\begin{gathered} P(A)=0.5 \\ P(B)=0.25 \\ P(A\cap B)=0.185 \end{gathered}$

And we have to find:

$P(A\cup B)$

We can calculate it using the expression:

$\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=0.5+0.25-0.185 \\ P(A\cup B)=0.565 \end{gathered}$

Answer: P(A or B) = 0.565.

NOTE: We can convert 0.565 in a fraction as:

$0.565=\frac{565}{1000}=\frac{113}{200}$

So 0.565 is equal to 113/200.