Transcript P(A B)

Probability
P(A)=n(A)/n(S)
n(AB)=n(A)+n(B)-n(AB)
P(AB)=P(A)+P(B)-P(AB)
Some terminology and their diagrams
At most one of A and B
Exactly one of A and B
At least one of A and B
Both A and B
Conditional Probability
P(A/B)=P(AB)/P(B)
Where P(A/B) is defined as the probability of occurrence
of event A given that event B has already occurred
Independent Events
If event A is independent of B
P(A/B)=P(A)
P(AB)=P(A)P(B)
and similarly
P(A1A2A3………..)=P(A1)P(A2)P(A3)…………
The result
P(A1A2  A3………..)=1P(A`1)P(A`2)P(A`3)…………
follows from the previous one.
Mutually Exclusive Events
P(AB)=0
P(AB`)=P(A)- P(AB)
By Venn diagran
Geometrical methods of probability
P{xA}=Measure of region A/Measure of samplespace
Baye’s Theorem
n(A)=n(AiA) where I varies from 1 to r
P(A)=P(AiA) where I varies from 1 to r
= P(Ai/A)P(A)
Inverse probability
P(Ai/A)= P(AiA) /P(A)=P(A/Ai).P(Ai)/ P(Ai/A)P(A)
Binomial Probability
N successive independent events
having only two results P and Q with
probability p and 1-p then the
probability of r P’s will be
P(E)= nCrpr(1-p) n-r
Q. A and B are two events .The
probability that at most one of A,B
occurs is
(a)1- P(AB)
(b)P(A’)+P(B’)- P(A’B’)
(c)P(A’)+P(B’)+ P(AB)-1
(d) P(AB’)+ P(A’B)+ P(A’B’)
Q.Three numbers are selected at random
without replacement from the set of the
numbers {1,2,….n}.The conditional
probability that the third number lies
between the first two number is known to be
smaller than the second is
(a)1/6
(b)1/3
(c)1/2
(d)none of these
Q.Seven digits from the numbers
1,2,3,4,5,6,7,8,9 are written in random
order,the probability that this seven digit
number is divisible by 9 is ___________.
JEE 2005
Screening Question:
Q.A six faced fair dice is thrown until
1 comes, then the probability that 1
comes in even no. of trials is
(a)5/11
(b)5/6
(c)6/11
(d)1/6
Mains Question
Q.A person goes to office either by
car,scooter,bus or train probability of
which being 1/7,3/7,2/7,and 1/7
respectively.Probability that he reaches
office late,if he takes car,scooter,bus or
train is 2/9,1/9,4/9 and 1/9
respectively.Given that he reached
office in time,then what is the
probability that he travelled by a car.