If A- B and C are three events such that PB-1-2- PA- B- C-1-3 and PA- B- C-1-336 then PB- C is equal to -

The correct option is B 3302016 P(B)=1/2P(A #8745;B #8745;C #8242;)=1/3P(A #8745;B) P(A #8745;B #8745;C)=1/3P(A #8242; #8745;B #8745;C ...

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Byju's Answer

Standard XII

Mathematics

Complement of an Event

If A, B and...

Question

If $A, B$ and $C$ are three events such that $P (B) = \frac{1}{2}$ ; $P (A \cap B \cap C^{'}) = \frac{1}{3}$ and $P (A^{'} \cap B \cap C^{'}) = \frac{1}{336}$ then $P (B \cap C)$ is equal to ...

\frac{328}{2016}

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\frac{330}{2016}

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\frac{324}{2016}

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\frac{320}{2016}

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Solution

The correct option is B $\frac{330}{2016}$
P(B)=1/2
P(A∩B∩C′)=1/3
P(A∩B)-P(A∩B∩C)=1/3

P(A′∩B∩C′)=1/336
P(only B)=1/336
P(B)-P(A∩B)-P(B∩C)+P(A∩B∩C)=1/336
1/2-1/3-P(B∩C)=1/336
P(B∩C)=1/6-1/336=330/2016

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Similar questions

If A, B and C are three events such that P(B) = $\frac{3}{4}, P (A \cap B \cap C^{'}) = \frac{1}{3} a n d P (A^{'} \cap B \cap C^{'}) = \frac{1}{3},$ then $P (B \cap C)$ is equal to

Q. If A, B and C are three events such that

P (B) = \frac{3}{4}, P (A \cap B \cap C^{'}) = \frac{1}{3}

and

P (A^{'} \cap B \cap C^{'}) = \frac{1}{3}

, then

P (B \cap C)

is equal to

Q. Assertion :If A, B, C are three events such that

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

P (B) = \frac{1}{6}

P (C) = \frac{2}{3}

then events A, B, C are mutually exclusive. Reason: If

P (A \cup B \cup C) = P (A) + P (B) + P (C)

then A, B, C are mutually exclusive events.

Q. If A and B are any two events such that P (A) + P (B) − P (A and B) = P (A), then (A) P (B|A) = 1 (B) P (A|B) = 1 (C) P (B|A) = 0 (D) P (A|B) = 0

Q. If

A, B, C

are three events, then show that

P (A \cup B \cup C) = P (A) + P (B) + P (C) - P (A \cap B) - P (B \cap C) - P (C \cap A) + P (A \cap B \cap C)

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If A,B and C are three events such that P(B)=12; P(A∩B∩C′)=13 and P(A′∩B∩C′)=1336 then P(B∩C) is equal to ...

The correct option is B 3302016P(B)=1/2P(A∩B∩C′)=1/3P(A∩B)-P(A∩B∩C)=1/3P(A′∩B∩C′)=1/336P(only B)=1/336P(B)-P(A∩B)-P(B∩C)+P(A∩B∩C)=1/3361/2-1/3-P(B∩C)=1/336P(B∩C)=1/6-1/336=330/2016

If $A, B$ and $C$ are three events such that $P (B) = \frac{1}{2}$ ; $P (A \cap B \cap C^{'}) = \frac{1}{3}$ and $P (A^{'} \cap B \cap C^{'}) = \frac{1}{336}$ then $P (B \cap C)$ is equal to ...

The correct option is B $\frac{330}{2016}$
P(B)=1/2
P(A∩B∩C′)=1/3
P(A∩B)-P(A∩B∩C)=1/3

P(A′∩B∩C′)=1/336
P(only B)=1/336
P(B)-P(A∩B)-P(B∩C)+P(A∩B∩C)=1/336
1/2-1/3-P(B∩C)=1/336
P(B∩C)=1/6-1/336=330/2016