Question

A bag contains 10 marbles: 4 are green, 2 are red, and 4 are blue. Christine chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are blue? Write your answer as a fraction in simplest form.

Answer 1

1st marble is blue is 4/10
2nd marble is blue is 3/9
Multiple together and the probability is 12/90 or 2/15

Answer 2

The probability that both marbles she chooses are blue is
`(2)/(15)`

Explanation:

Given : A bag contains 10 marbles: 4 are green, 2 are red, and 4 are blue. Christine chooses a marble at random, and without putting it back, chooses another one at random.

To find : What is the probability that both marbles she chooses are blue?

Solution :

Total number of marbles = 10

Green marbles = 4

Red marbles = 2

Blue marbles = 4

Probability is favorable outcome upon total number of outcomes.

Probability of getting first marble is blue

`\text{P(first blue marble)}=(4)/(10)=(2)/(5)`.

Without replacement,

i.e. Blue marble left = 3

Total marble left = 9

Probability of getting second marble is blue

`\text{P(second blue marble)}=(3)/(9)=(1)/(3)`

The probability that both marbles she chooses are blue is

`\text{P(both blue marble)}=(2)/(5)*(1)/(3)`

`\text{P(both blue marble)}=(2)/(15)`

Therefore, The probability that both marbles she chooses are blue is
`(2)/(15)`