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Standard XII

Mathematics

Total Probability Theorem

A and B are t...

Question

A and B are two events such that P(A) = 0.25 and P(B) = 0.50. The pobability of both happening together is 0.14. The probability of both A and B not happening is

0.39

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0.25

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0.11

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none of these

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Solution

The correct option is A
0.39

$P (A) = 0.25$ and $P (B) = 0.50$

$P (A \cap B) = 0.14$

$∴$ Required probability $= 1 - P (A \cap B)$

$= 1 - [P (A) + P (B) - P (A \cap B)]$

$= 1 - [0.25 + 0.50 - 0.14]$

$= 1 - 0.61 = 0.39$

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Similar questions

Q. A and B are two events such that P (A) = 0.25 and P (B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is
(a) 0.39
(b) 0.25
(c) 0.11
(d) none of these

A

and

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are two events where

P (A) = 0.25

and

P (B) = 0.5

. The probability of both happening together is

0.14

. The probability of both

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and

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The probability of happening of two events A and B are 0.25 and 0.50 respectively. If the probability of happening of A and B together is 0.14, then probability that neither A nor B happens is

Q. The probabilities of happening of two events A and B are 0.25 and 0.50 respectively. If the probability of happening of A and B together is 0.14, then probability that neither A nor B happens is
(a) 0.39
(b) 0.25
(c) 0.11
(d) none of these

A

and

B

are two events such that

P (A) = 0.3, P (B) = 0.8

and

P (A \cap B) = 0.16

. Find the probability that exactly one of the events happens.

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A and B are two events such that P(A) = 0.25 and P(B) = 0.50. The pobability of both happening together is 0.14. The probability of both A and B not happening is

The correct option is A 0.39 P(A)=0.25 and P(B)=0.50 P(A∩B)=0.14 ∴ Required probability =1−P(A∩B) =1−[P(A)+P(B)−P(A∩B)] =1−[0.25+0.50−0.14] =1−0.61=0.39

The correct option is A
0.39

$P (A) = 0.25$ and $P (B) = 0.50$

$P (A \cap B) = 0.14$

$∴$ Required probability $= 1 - P (A \cap B)$

$= 1 - [P (A) + P (B) - P (A \cap B)]$

$= 1 - [0.25 + 0.50 - 0.14]$

$= 1 - 0.61 = 0.39$