Probability

A. 1/6
B. 5/8
C. 3/8
D. 5/6
Explanation:
P(at least one graduate) = 1 – P(no graduates) =
1 – ⁶C₃/¹⁰C₃ = 1 – (6 * 5 * 4)/(10 * 9 * 8) = 5/6

A. 18/35
B. 12/35
C. 17/35
D. 19/35
Explanation:
If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35

A. 5/21
B. 5/14
C. 9/14
D. 16/21
Explanation:
Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅
= (10 * 6)/252 = 5/21

A. 0.4869
B. 0.5904
C. 0.6234
D. 0.5834
Explanation:
P(winning prize atleast on one ticket)
= 1 – P(“Losing on all tickets”)
= 1 – (0.8)4 = (1 + (0.8)2)(1 – (0.8)2)
= (1.64)(0.36) = 0.5904

A. 1/10
B. 9/10
C. 1/5
D. 3/10
Explanation:
10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5

A. 0
B. 1/7
C. 2/7
D. 5/7
Explanation:
A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7

A. 10/17
B. 10/19
C. 46/105
D. Cannot be determined
Explanation:
There is no definite formula for finding prime numbers among 15 consecutive numbers. Hence the probability cannot be determined.

A. 4/9
B. 5/9
C. 7/9
D. 8/9
Explanation:
Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.
The required probability = (5 * 4)/⁹C₂ = 20/36 = 5/9

A. 3/22
B. 4/21
C. 2/21
D. 1/14
Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21

A. 1/455
B. 2/455
C. 1/91
D. 4/455
Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13) = 1/455