ProbabilityHard
Question
Let A & B be two independent events of an experiment such that B is twice as likely to occur as A. If P(A) denotes the probability of occurence of A where P(A) ∈ [a,b] then a + 
is equal to -
is equal to -Options
A.4
B.2
C.even
D.prime
Solution
Let P(A) = x
⇒ P(B) = 2x
Now P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= P(A) + P(B) - P(A).P(B) = x + 2x - 2x2
Now 0 ≤ P(A ∪ B) ≤ 1
⇒ 0 ≤ 3x - 2x2 ≤ 1
⇒ x ∈
⇒ a + 
= 4
⇒ P(B) = 2x
Now P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= P(A) + P(B) - P(A).P(B) = x + 2x - 2x2
Now 0 ≤ P(A ∪ B) ≤ 1
⇒ 0 ≤ 3x - 2x2 ≤ 1
⇒ x ∈
⇒ a + = 4Create a free account to view solution
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