Question on: JAMB Mathematics - 2015

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

\( \frac{2}{15} \)

\( \frac{3}{4} \)

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

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

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Correct Option: C

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}{15} ) + ( \frac{1}{3} ) − ( \frac{1}{15} )

= (3 + 5 + 1) ÷ 15

= ( \frac{7}{15} )