Answer to Question #183111 in Statistics and Probability for Kyle

Question

A group of 10 students is used for an experimental study. The group comprises of 3 students with blood type O, 4 with blood type A, and 3 with blood type B. What is the probability that a random sample of 5 will contain 1 student with blood type O, 2 students with blood type A, and 2 students with blood type B?

Answer 1

We have,

A group of 10 student

Out of which 3 students with blood type O, 4 with blood type A, and 3 with blood type B

We have to select 5 students from the group of 10.

Then, Number of Ways $= ^{10}C_5 = 252$

Hence, The probability that a random sample of 5 will contain 1 student with blood type O, 2 students with blood type A, and 2 students with blood type B

$= \dfrac{^3C_1 \times ^4C_2 \times ^3C_2}{^10C_5}$

$= \dfrac{3 \times 6 \times 3}{252}$

$= \dfrac{3}{14}$