Answer to Question #163381 in Statistics and Probability for Nomhle Lukashe

Question

. A housewife is asked to rank five brands of washing powder (A, B, C, D, E) in order of preference. Suppose that she actually has no preference and her ordering is arbitrary. What is the probability that: (a) brand A is ranked first; (b) brand C is ranked first and brand D is ranked second.

Answer 1

Solution:

a.

Total number of different combinations of rankings: $5!$

A is fixed on the first spot, so the total number of rankings with A on the first spot is $1*4*3*2*1=4!$

$P(A****) = \frac{4!}{5!}= 1/5=0.2$

b.

Total number of different combinations of rankings: $5!$

We fix C on the first place, and D on the second place, so number of remaining combinations with C on 1st and D on 2nd:

$1*1*3*2*1=3!$

$P(CD***)=\frac{3!}{5!}=1/20=0.05$

Answer:

a. $P(A****) = \frac{4!}{5!}= 1/5=0.2$

b. $P(CD***)=\frac{3!}{5!}=1/20=0.05$