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# The probability of an event A is 1/5. The probability of B is 1/3 . The probabilit...

### Question

The probability of an event A is 1/5. The probability of B is 1/3 . The probability both A and B is 1/15. What is the probability of either event A or B or both?

### Options

A) $$\frac{2}{15}$$

B) $$\frac{3}{4}$$

C) $$\frac{7}{15}$$

D) $$\frac{1}{15}$$

### Explanation:

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 is prob (A ∪ B) = ∩ prob(A) + prob(A) − prob(A ∩ B)
II. But if the probability of both outcomes A and B
The formula 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) = $$\frac{1}{15}$$ + $$\frac{1}{3}$$ − $$\frac{1}{15}$$
= (3 + 5 + 1) ÷ 15
= $$\frac{7}{15}$$

## Dicussion (1)

• 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 is prob (A ∪ B) = ∩ prob(A) + prob(A) − prob(A ∩ B)
II. But if the probability of both outcomes A and B
The formula 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) = $$\frac{1}{15}$$ + $$\frac{1}{3}$$ − $$\frac{1}{15}$$
= (3 + 5 + 1) ÷ 15
= $$\frac{7}{15}$$