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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) \( \frac{1}{15} \)

The correct answer is C.

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
= \( \frac{7}{15} \)

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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
    = \( \frac{7}{15} \)

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