Answer to Question #212877 in Statistics and Probability for Spencer

Question

Q1. A box contains 4 white balls, 3 red balls and 3 blue balls.A ball is selected at random and its colour is written down . It is replaced each time .Find the probability that if 6 balls are selected, 3 are white , 2 are red and 1 is blue.

Q2. Out of 4 students, level 100 ,a level 200 , a level 300 and a level 400. Two of them are to be chosen to perform a certain task . What is the probability that a level 200 student would be chosen if selection is done at random?

Answer 1

Q1

The sample space is {4W, 3R and 3B}.

The number of total outcomes is n=4+3+3=10

Then the probability to find a white ball is $\frac{4}{10}$ , the probability of a red ball is $\frac{3}{10}$ and the probability of a blue ball is $\frac{3}{10}$

Since we're extracting with replacement, those events are independent and the probability for getting 3 white, 2 red and 1 blue balls is as follows:

$P = (\frac{4}{10})^3(\frac{3}{10})^2(\frac{3}{10}) = 0.001728$

There are $\frac{6!}{3!2!1!} =60$ ways to get 3 white, 2 red and 1 blue balls

$P=60 \times 0.001728 = 0.10368$

Q2

N=4

n=2

Number of samples $= \frac{N!}{n!(N-n)!}$

$= \frac{4!}{2!(4-2)!}= \frac{3 \times 4}{2}= 6$

Samples:

1. 100, 200

2. 100, 300

3. 100, 400

4. 200, 300

5. 200, 400

6. 300, 400

P(a level 200 student would be chosen) $= \frac{3}{6}= \frac{1}{3}$