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Theoretical Probability

What is inter...

Question

What is intersaction of 2 events? Formula for P(A^B)?

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Solution

Dear student,
An intersection of two events means that the common part of two events. That is if A and B are two events then
A $\cap$ B denotes the common part of it. A $\cap$ B $\subset$ A, and A $\cap$ B $\subset$ B.
Now P(A $\cup$ B)=P(A)+P(B)-P (A $\cap$ B) so P (A $\cap$ B) = P(A)+P(B)- P(A $\cup$ B)
But if two events are independent of each other then you can find P (A $\cap$ B) just by multiplying the probabilities of those two events. i.e. P (A $\cap$ B)=P(A).P(B)
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Q. If A and B are two events such that A ≠ Φ, B = Φ, then

(a)

P (\frac{A}{B}) = \frac{P (A \cap B)}{P (B)}

P (\frac{A}{B}) = P (A) P (B)

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

P (\frac{A}{B}) = \frac{P (A)}{P (B)}

Q. A and B are two events such that

P (A + B) = \frac{5}{6}, P (A B) = \frac{1}{3}, P (B) = \frac{1}{2},

then the event A and B are

A

B

are two events such that

P (A) = 0.2

P (A B) = 0.7

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B

are independent events then

P (B)

Q. If two events

A

B

P (A^{'}) = 0.3, P (B) = 0.4

P (A B^{'}) = 0.5

P (\frac{B}{(A \cup B^{'})}) =

If A and B are two events such that ,

[MP PET 1992]

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