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Axiomatic Approach

Let E 1 and E...

Question

Let $E_{1}$ and $E_{2}$ be two independent events such that $P (E_{1}) = P_{1}$ and $P (E_{2}) = P_{2}$ . Describe in words of the events whose probabilities are

$P_{1} + P_{2} - 2 P_{1} P_{2}$

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Solution

$P (E_{1}) = P_{1}$ and $P (E_{2}) = P_{2}$

$P_{1} + P_{2} - 2 P_{1} P_{2} = P (E_{1}) + P (E_{2}) - 2 P (E_{1}) . P (E_{2}) = P (E_{1}) + P (E_{2}) - 2 P (E_{1} \cap E_{2}) = P (E_{1} \cup E_{2}) - P (E_{1} \cap E_{2})$
So, either $E_{1}$ or $E_{2}$ occurs but not both.

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p₂) (iv) p₁ + p₂

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