Types of Probability Questions
In previous articles we have already understood the basic concepts of Probabilty, and have also see some very basic question types.
In this article, we are going to have a look at some other kinds of questions formed on the topic of Probabilty.
Type 1: Probability in Selection
Q. A committee of two members is to be chosen from a group of 5 men and 4 women. Out of the 9 people, there is one couple. What is the probability that the committee has one male and one female member if the couple cannot be in the committee simultaneously?
(a) 5/18 (b) 19/36 (c) 21/36 (d) 1/20
Explanation:
Number of ways of choosing a committee of two members = $C^9_2$ = (9 × 8)/2 = 36
Number of ways of choosing a committee of one male and one female members = 5 × 4 = 20
Number of ways of choosing a committee such that the members are the couple = 1
Number of ways of choosing the committee of one male and one female such that the couple is not in the committee simultaneously = 20 – 1 = 19
So, Required probability = 19/36
Answer: (b)
Type 2: Probability in Arrangement
Q. Four boys and eight girls are sitting in a row. What is the probability that all the girls are sitting together?
(a) 4!/8!
(b) (6! × 8!)/12!
(c) (5! × 8!)/12!
(d) 5!/12!
Explanation:
Total number of arrangements possible = 12!
Eight girls can sit together if they are considered as a block. Number of ways of such arrangement = (4 + 1)! = 5!
Number of ways in which those 8 girls can sit among themselves = 8!
Hence, number of ways in which 4 boys and 8 girls sit such that all girls sit together = 5! × 8!
Required probability = (5! × 8!)/12!
Answer: (c)