find the probability that event a or b will occur.\np(a or b) = ?

Answer:

$\frac{13}{15}$

Explanation:

Step1: Recall probability formula

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Step2: Calculate $P(A)$

$P(A)=\frac{2}{15}+\frac{7}{15}=\frac{9}{15}$

Step3: Calculate $P(B)$

$P(B)=\frac{7}{15}+\frac{4}{15}=\frac{11}{15}$

Step4: Calculate $P(A\cap B)$

$P(A\cap B)=\frac{7}{15}$

Step5: Substitute values

$P(A\cup B)=\frac{9}{15}+\frac{11}{15}-\frac{7}{15}=\frac{9 + 11-7}{15}=\frac{13}{15}$