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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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Q. Let A and B be two independent events such that P(A) = p₁ and P(B) = p₂. Describe in words the events whose probabilities are:

(i) p₁p₂ (ii) (1

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p₁)p₂ (iii) 1

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p₂) (iv) p₁ + p₂

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2p₁p₂ [NCERT EXEMPLAR]

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}) =

E_{1}

E_{2}

are two events such that

P (E_{1}) = \frac{1}{4}, P (\frac{E_{2}}{E_{1}}) = \frac{1}{2}

P (\frac{E_{1}}{E_{2}}) = \frac{1}{4},

then which of the following is/are correct?

P (E_{1}) = 0.2, P (E_{2}) = 0.4

P (E_{3}) = 0.6

E_{1}, E_{2}

E_{3}

are independent events, then the probability that at least one of these events

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E_{3}

E_{1}

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are two events such that

P (E_{1}) = \frac{1}{4}

P (\frac{E_{2}}{E_{1}}) = \frac{1}{2}

P (\frac{E_{1}}{E_{2}}) = \frac{1}{4}

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