Question

There is a bag filled with 4 blue and 5 red marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 blues?,

Answer 1

Answer:

16.67% probability of getting 2 blues

Step-by-step explanation:

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

The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

What is the probability of getting 2 blues?

Desired outcomes:

Two blue marbles, from a set of 4.

$D = C_{4,2} = \frac{4!}{2!(4-2)!} = 6$

Total outcomes:

Two marbles, from a set of 9.

$T = C_{9,2} = \frac{9!}{2!(9-2)!} = 36$

Probability:

$p = \frac{D}{T} = \frac{6}{36} = 0.1667$

16.67% probability of getting 2 blues