Question

—statistics and probability, rules of probability

Question:
Mary has 10 blouses hanging in her closet— 5 are blue, 2 are black, and the rest are red. if she hangs the blouse in a random order, what is the probability that the first and last blouse are both red?

A. 0.011
B. 0.067
C. 0.042
D. 0.001
​

Answer 1

B. 0.067

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Number of arrangements:

The number of possible arrangements of n elements is given by:

`A_(n) = n!`

Desired outcomes

First red(10 - (5+2) = 3 possible)

Last red(2 possible).

Middle 8 arranged in any way.

So

`D = 3*A_(8)*2 = 3*8!*2 = 241920`

Total outcomes:

Arrangements of 10 elements. So

`T = A_(10) = 10! = 3628800`

What is the probability that the first and last blouse are both red?

`p = (D)/(T) = (241920)/(3628800) = 0.067`

The correct answer is given by option B.