Given:
Number of red marbles = 5
Number of blue marbles = 4
Number of yellow marbles = 3
To find:
The probability of pulling a red marble, then pulling a blue marble, without replacement.
Solution:
Probability formula:
[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
We have,
Number of red marbles = 5
Total number of marbles is:
[tex]5+4+3=12[/tex]
Probability of getting a red marble is:
[tex]P(Red)=\dfrac{5}{12}[/tex]
After selecting one red marble, the remaining number of marbles is 11 and the number of blue marbles is 3. So,
[tex]P(Blue)=\dfrac{4}{11}[/tex]
Now, the probability of pulling a red marble, then pulling a blue marble, without replacement is:
[tex]\text{Probability percentage}=P(Red)\times P(Blue)\times 100[/tex]
[tex]\text{Probability}=\dfrac{5}{12}\times \dfrac{4}{11}\times 100[/tex]
[tex]\text{Probability}=15.1515...[/tex]
[tex]\text{Probability}\approx 15.2\%[/tex]
Therefore, the correct option is B.
