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Engineering Mathematics

Independent and Dependent Events

E1 and E2 are...

Question

$E_{1} a n d E_{2}$ are events in a probability space satisfying the following constraints $P (E_{1}) = P (E_{2}); P (E_{1} \cup E_{2}) = 1; E_{1} a n d E_{2}$ are independent then $P (E_{1}) =$

A

0

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B

\frac{1}{4}

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C

\frac{1}{2}

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D

1

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Solution

The correct option is D 1
$L e t P (E_{1}) = P (E_{2}) = p$ then using Addition theorem of probability

$P (E_{1} \cup E_{2}) = P (E_{1}) + P (E_{2}) - P (E_{1} \cap E_{2})$

$[∵ i n c a s e o f i n d e p e n d e n t e v e n t s P (E_{1} \cap E_{2}) = P (E_{1}) P (E_{2})]$

$1 = p + p - p^{2}$
$o r p^{2} - 2 p + 1 = 0$
$o r p = 1$

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Similar questions

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E_{2}

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