ProbabilityHard
Question
For two given events A and B, P(A ∩ B) is
Options
A.not less that P(A) + P(B) - 1
B.not greater than P(A) + P(B)
C.equal to P(A) + P(B) - P(A ∪ B)
D.equal to P(A) + P(B) + P(A ∪ B)
Solution
We know that,
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Also, P(A ∪ B) ≤ 1
∴ P(A ∩ B)max = 1
⇒ P(A ∩ B) ≥ P(A) + P(B) - 1
∴ Option (a) is true.
Again, P(A ∪ B) ≥ 0
∴ P(A ∩ B)max, when P(A ∪ B)max, = 0
⇒ P(A ∩ B) ≤ P(A) + P(B)
∴ Option (b) is true.
Also, P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Thus, (c) is also correct.
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Also, P(A ∪ B) ≤ 1
∴ P(A ∩ B)max = 1
⇒ P(A ∩ B) ≥ P(A) + P(B) - 1
∴ Option (a) is true.
Again, P(A ∪ B) ≥ 0
∴ P(A ∩ B)max, when P(A ∪ B)max, = 0
⇒ P(A ∩ B) ≤ P(A) + P(B)
∴ Option (b) is true.
Also, P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Thus, (c) is also correct.
Create a free account to view solution
View Solution FreeMore Probability Questions
Two dice are thrown together. If 3 appears on at least one of the dice, then what is the probability that the sum is gre...Let 0 < P (A) < 1, 0 < P (B) < 1 and P(A υ B) = P (A) + P (B) - P (A) P (B). Then -...A man alternately tosses a coin and throws a dice beginning with the coin. The probability that he gets a head in the co...India plays two matches each with west and Australia. In any match the probabilities of India getting points 0, 1 and 2 ...A Urn contains ′m′ white and ′n′ black balls. Balls are drawn one by one till all the balls are ...