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Probability



Q1. An urn contains 9 balls two of which are red , three blue and four black . Three balls are drawn at random. The probability that they are of same colour is :

(a)
3/27


(b)
20/31


(c)
5/84


(d) None

Solution. c
In this case red ball will not be consider to drawn , because it has only 2 (in number) , and as per question all three balls should be of same colour .

So, Probability will be =
3C3/9C3
+
4C3/9C3


1/84
+
4/84


=
5/84
Solution

Q2. Probability that the event A occur, if
(i) The odds in favor are 3:2 and
(ii) The odds against it are 1:4

(a)
1/5
and
3/2


(b)
5/8
and
3/7


(c)
2/5
and
1/2


(d)
3/5
and
4/5

Solution. d
3/5
and
4/5
Solution

Q3. P(A) =
2/5
, P(B) =
7/10
, and P(A∩B) =
1/10
. what is P(B - A) + P(A - B)?

(a)
27/50


(b)
2/10


(c)
9/10


(d) None of these

Solution.c
= P(B - A) + P(A - B)

= P(B) - P(A∩B) + P(A) - P(A∩B)

= P(B) + P(A) - 2P(A∩B)

=
7/10
+
2/5
-
2/10


=
7/10
+
4/10
-
2/10


=
11/10
-
2/10
=
9/10
Solution

Q4. Forty percent of the student passed in statistics, 35% of the student passed in mathematics where as 40% failed in both the subject . If the student is selected at random, what is the probabilitythat he is passed in both the subject ?

(a) 0.20

(b) 0.15

(c) 0.18

(d) 0.5

Solution. b
P(A) = 0.40 , P(B) = 0.35

P(A'∩B') = 0.40

P(A∪B)' = 0.40

P(A∪B)= 0.60

P(A∪B) = P(A) + P(B) - P(A∩B)

0.60 = 0.40 + 0.35 - P(A∩B)

0.60 = 0.75 - P(A∩B)

-0.15 = -P(A∩B)

P(A∩B) = 0.15
Solution

Q5. The sum of numbers obtained in throw of a dice twice is S. Probability of S will be maximum if S is .

(a) 3

(b) 9

(c) 6

(d) 7

Solution.d
7
Solution