Question

what is the probability that either event a or event b will occur?
p(a) = \frac{13}{19}
p(b) = \frac{12}{19}
p(a and b) = \frac{10}{19}
p(a or b) = p(a) + p(b) - p(a and b)
p(a or b) = \frac{?}{19}

Explanation:

Step1: Substitute given values

$P(A)=\frac{13}{19}$, $P(B)=\frac{12}{19}$, $P(A\ and\ B)=\frac{10}{19}$ into the formula $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$.
$P(A\ or\ B)=\frac{13}{19}+\frac{12}{19}-\frac{10}{19}$

Step2: Calculate the sum and difference of fractions

$P(A\ or\ B)=\frac{13 + 12- 10}{19}=\frac{15}{19}$

Answer:

$\frac{15}{19}$