Question

Using a real life example explain where the formula for conditional probability [P(B|A) = P(A ∩B) P(A) ] comes from. Hence, or otherwise, explain why, for independent events, the probability of the two events both occurring is the same as the probability of the first event occurring multiplied by the second event occurring.

Answer #1

**P(B|A) = P(A ∩B) P(A)**

**EXAMPLE-**

In a card game, suppose a player needs to draw two cards of the
same suit in order to win. Of the 52 cards, there are 13 cards in
each suit. Suppose first the player draws a heart. Now the player
wishes to draw a second heart. Since one heart has already been
chosen, there are now 12 hearts remaining in a deck of 51 cards. So
the conditional probability *P(Draw second heart|First card a
heart)* = 12/51.

Suppose an individual applying to a college determines that he
has an 80% chance of being accepted, and he knows that dormitory
housing will only be provided for 60% of all of the accepted
students. The chance of the student being accepted *and*
receiving dormitory housing is defined by

*P(Accepted and Dormitory Housing) = P(Dormitory
Housing|Accepted)P(Accepted)* = (0.60)*(0.80) = 0.48.

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Bayes's Theorem is used to calculate the conditional probability
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occurred. The probability of event A given event B is expressed as
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MC0402: Suppose there are two events, A and B.
The probability of event A is P(A) = 0.3.
The probability of event B is P(B) = 0.4.
The probability of event A and B (both occurring) is P(A and B)
= 0.
Events A and B are:
a.
40%
b.
44%
c.
56%
d.
60%
e.
None of these
a.
Complementary events
b.
The entire sample space
c.
Independent events
d.
Mutually exclusive events
e.
None of these
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Consolidated Builders has bid on two large construction
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