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JAMB Mathematics 2015 Paper

Question : 32

Total: 61

Solution:

Concept:

The probability of

A

B

or both means the union of events

A

and

B

, written as

P(A \cup B)

Explanation:

Since the events can occur together, use the inclusion-exclusion formula:

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

Substitute the given values:

P(A) = \frac{1}{5},\quad P(B) = \frac{1}{3},\quad P(A \cap B) = \frac{1}{15}

Therefore,

P(A \cup B) = \frac{1}{5} + \frac{1}{3} - \frac{1}{15}

Use a common denominator of

15

\frac{3}{15} + \frac{5}{15} - \frac{1}{15} = \frac{7}{15}

So the probability is

\frac{7}{15}

, which is not listed among the options.

Answer:

P(A \text{ or } B \text{ or both}) = \frac{7}{15}

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