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Question
Fill in the blank in the table:
| P (A) | P (B) | P (A ∩ B) | P(A∪ B) |
| \[\frac{1}{3}\] | \[\frac{1}{5}\] | \[\frac{1}{15}\] | ...... |
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Solution
Given: \[P\left( A \right) = \frac{1}{3}, P\left( B \right) = \frac{1}{5} \text{ and } P\left( A \cap B \right) = \frac{1}{15}\]
By addition theorem, we have:
P (A ∪ B) = P(A) + P (B) - P (A ∩ B)
\[= \frac{1}{3} + \frac{1}{5} - \frac{1}{15}\]
\[= \frac{5 + 3 - 1}{15} = \frac{7}{15}\]
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