Prob(A) = \( \frac{1}{5} \) , Prob(B) = \( \frac{1}{4} \), Prob (A ∩ B) = \( \frac{1}{15} \), Prob (A ∪ B) = ?
Note:
I. the probability is either event of A or B or both.
The formula using is prob (A ∪ B) = ∩ prob(A) + prob(A) − prob(A ∩ B)
II. But if the probability of both outcomes A and B
The formula using is Prob(A ∩ B) − prob(A) + prob(B) – prob (A ∪ B)
In this question, A or B, Prob (A ∩ B): A and B, Prob (A ∩ B)
prob (A ∪ B) = prob(A) + prob(B) − Prob (A ∩ B) is used.
prob (A ∪ B) = \( \frac{1}{5} \) + \( \frac{1}{3} \) − \( \frac{1}{15} \)
= (3 + 5 - 1) ÷ 15
= \( \frac{7}{15} \)