Given:
Number of red marbles = 4
Number of blue marbles = 8
Number of yellow marbles = 6
Number of green marbles = 2
To find:
The probability of getting a blue marble then a red marble, i.e., P(blue, red).
Solution:
Using the given information,
The total number of marbles = 4+8+6+2
= 20
Probability of getting a blue marble in first draw is
[tex]P(Blue)=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}[/tex]
[tex]P(Blue)=\dfrac{8}{20}[/tex]
[tex]P(Blue)=\dfrac{2}{5}[/tex]
Maria selects a marble, puts it back and then selects a second marble. It means the total number of marbles remains the same.
[tex]P(red)=\dfrac{\text{Number of red marbles}}{\text{Total number of marbles}}[/tex]
[tex]P(red)=\dfrac{4}{20}[/tex]
[tex]P(red)=\dfrac{1}{5}[/tex]
Now, the probability of getting a blue marble then a red marble is
[tex]P(blue,red)=\dfrac{2}{5}\times \dfrac{1}{5}[/tex]
[tex]P(blue,red)=\dfrac{2}{25}[/tex]
Therefore, the required probability P(blue, red) is [tex]\dfrac{2}{25}[/tex].
