Question

let a and b be two events with p(a) = $\frac{4}{5}$, p(b) = $\frac{3}{8}$, and p(a and b) = $\frac{3}{10}$. what is p(a or b)? write your answer as a fraction or decimal. do not round.

Explanation:

Step1: Recall the formula

$P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$

Step2: Substitute the given values

$P(A)=\frac{4}{5}$, $P(B)=\frac{3}{8}$, $P(A\ and\ B)=\frac{3}{10}$
$P(A\ or\ B)=\frac{4}{5}+\frac{3}{8}-\frac{3}{10}$

Step3: Find a common - denominator

The common denominator of 5, 8, and 10 is 40.
$\frac{4}{5}=\frac{4\times8}{5\times8}=\frac{32}{40}$, $\frac{3}{8}=\frac{3\times5}{8\times5}=\frac{15}{40}$, $\frac{3}{10}=\frac{3\times4}{10\times4}=\frac{12}{40}$

Step4: Calculate the sum

$P(A\ or\ B)=\frac{32}{40}+\frac{15}{40}-\frac{12}{40}=\frac{32 + 15-12}{40}=\frac{35}{40}=\frac{7}{8}$

Answer:

$\frac{7}{8}$