Probability
Q1.
If A and B are two independent events and P(A∪B) =
2/5
, P(B) =
1/3
. Find P(A) .
(a) 1/10
(b) 2/9
(c) - 1/2
(d) 3/4
Solution. a
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = P(A) + P(B) - P(A) . P(B) -----------(1)
or
P(A∪B) = P(A) + P(B) {1 - P(A)} -----------
(2)
or
= P(A) + P(B). P(A') -----------(3)
Apply anyone equation to get this answer
Let P(A) = x ,
2/5
= x +
2/5
= x +
1/3
. (1 - x)
2/5
= x +
1/3
-
x/3
⇒
2/5
-
1/3
=
2x/3
1/15
=
2x/3
⇒
x =
1/10
Solution
Q2.
A dice tossed once and A is a event to get less than 3 , find the probablity of P(A∪A')
(a) 0.5
(b) 0
(c) 1
(d) 1/3
Solution. c
P(A∪A') = P(S) = 1
Note : As we know that P(A∪A') are exhaustive events. So ,
(A∪A') = S (sample space)
Solution
Q3.
If P(A∩B) = P(A) , find A∪B .
(a) P(A)
(b) P(B)
(c) 1
(d) 0
Solution. b
Because A is a subset of B .
Solution
Q4.
There are two events are A1 and A2 . P( A1) = 2/5 and P( A2) = 5/8 and P( A1
∩ A2) = 1/4 , Then A1 A2 are .
(a) Mutually exclusive but not independent events
(b) Mutually exclusive and independent events
(c) Independent but not mutually exclusive events
(d) None of these
Solution. C
Note: (i) in the case of independent events P(A∩B) = P(A).P(B)
(ii) in the case of mutually exclusive events P(A∪B) = 0
Solution
Q5.
If P(
A/B
) = P(A) .
(a) Event A and B are independent event .
(b) Mutually exclusive event.
(c) exhaustive event
(d) None of these
Solution. a
Event A and B are independent event .
Solution
