CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Intersection of Sets

A,B,C are any...

Question

$A, B, C$ are any three events. If $P (S)$ denotes the probability of $S$ happening, then $P (A \cap (B \cup C)) =$

A

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

P (A) + P (B) + P (C) - P (B) P (C)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $P (A \cap B) + P (A \cap C) - P (A \cap B \cap C)$
$P (A \cap (B \cup C)) = P [(A \cap B) \cup (A \cap C)] = P (A \cap B) + P (A \cap C) - P [(A \cap B) \cap (A \cap C)] = P (A \cap B) + P (A \cap C) - P (A \cap B \cap C)$

Suggest Corrections

thumbs-up

0

Similar questions

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)

A, B, C

are three events 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)

Q. The probabilities of three events

A, B

C

P (A) = 0.6, P (B) = 0.4, P (C) = 0.5

P (A \cup B) = 0.8, P (A \cap C) = 0.3, P (A \cup B \cup C) \geq 0.85, P (A \cap B \cap C) = 0.2

P (B \cap C) = p_{1}

A, B

C

be three events such that

P (A) = 0.3, P (B) = 0.4, P (C) = 0.8, P (A \cup B) = 0.08, P (A \cap C) = 0.28, P (A \cap B \cap C) = 0.09

P (A \cup B \cup C) \geq 0.75

P (B \cap C)

A, B

C

are three events such that

P (A) = 0.3, P (B) = 0.4, P (C) = 0.8

P (A \cap B) = 0.12, P (A \cap C) = 0.28

P (A \cap B \cap C) = 0.09

P (A \cup B \cup C) \geq 0.75

, then the limits of

P (B \cap C)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Intersection of Sets

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon