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
![P(Blue)=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}](https://tex.z-dn.net/?f=P%28Blue%29%3D%5Cdfrac%7B%5Ctext%7BNumber%20of%20blue%20marbles%7D%7D%7B%5Ctext%7BTotal%20number%20of%20marbles%7D%7D)
![P(Blue)=\dfrac{8}{20}](https://tex.z-dn.net/?f=P%28Blue%29%3D%5Cdfrac%7B8%7D%7B20%7D)
![P(Blue)=\dfrac{2}{5}](https://tex.z-dn.net/?f=P%28Blue%29%3D%5Cdfrac%7B2%7D%7B5%7D)
Maria selects a marble, puts it back and then selects a second marble. It means the total number of marbles remains the same.
![P(red)=\dfrac{\text{Number of red marbles}}{\text{Total number of marbles}}](https://tex.z-dn.net/?f=P%28red%29%3D%5Cdfrac%7B%5Ctext%7BNumber%20of%20red%20marbles%7D%7D%7B%5Ctext%7BTotal%20number%20of%20marbles%7D%7D)
![P(red)=\dfrac{4}{20}](https://tex.z-dn.net/?f=P%28red%29%3D%5Cdfrac%7B4%7D%7B20%7D)
![P(red)=\dfrac{1}{5}](https://tex.z-dn.net/?f=P%28red%29%3D%5Cdfrac%7B1%7D%7B5%7D)
Now, the probability of getting a blue marble then a red marble is
![P(blue,red)=\dfrac{2}{5}\times \dfrac{1}{5}](https://tex.z-dn.net/?f=P%28blue%2Cred%29%3D%5Cdfrac%7B2%7D%7B5%7D%5Ctimes%20%5Cdfrac%7B1%7D%7B5%7D)
![P(blue,red)=\dfrac{2}{25}](https://tex.z-dn.net/?f=P%28blue%2Cred%29%3D%5Cdfrac%7B2%7D%7B25%7D)
Therefore, the required probability P(blue, red) is
.