Answer:
The probability that both marbles she chooses are blue is [tex]\frac{2}{15}[/tex]
Step-by-step 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
[tex]\text{P(first blue marble)}=\frac{4}{10}=\frac{2}{5}[/tex].
Without replacement,
i.e. Blue marble left = 3
Total marble left = 9
Probability of getting second marble is blue
[tex]\text{P(second blue marble)}=\frac{3}{9}=\frac{1}{3}[/tex]
The probability that both marbles she chooses are blue is
[tex]\text{P(both blue marble)}=\frac{2}{5}\times\frac{1}{3}[/tex]
[tex]\text{P(both blue marble)}=\frac{2}{15}[/tex]
Therefore, The probability that both marbles she chooses are blue is [tex]\frac{2}{15}[/tex]
