Answer:
![\frac{3}{19}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B19%7D)
Step-by-step explanation:
Given :
A bag contains 10 blue, 6 green, and 4 red marbles.
You choose one marble. Without putting it back, you choose a second marble.
To Find: What is the probability that you first choose a green marble and then a blue marble?
Solution:
No. of blue balls = 10
No. of green balls =6
No. of red marbles =4
Total no. of marbles = 10+6+4 =20
Since we are given that first he choose a green marble
So, probability of getting green marble :
![\frac{\text{No. of green marbles}}{\text{total no. of marbles}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BNo.%20of%20green%20marbles%7D%7D%7B%5Ctext%7Btotal%20no.%20of%20marbles%7D%7D)
= ![\frac{6}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B20%7D)
Since he choose second marble without replacement
So, after choosing first ball . The total no. of balls will be 19
So, Probability of getting blue marble in second draw :
![\frac{\text{No. of blue marbles}}{\text{total no. of marbles}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BNo.%20of%20blue%20marbles%7D%7D%7B%5Ctext%7Btotal%20no.%20of%20marbles%7D%7D)
= ![\frac{10}{19}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B19%7D)
The probability that you first choose a green marble and then a blue marble:
![=\frac{6}{20}*\frac{10}{19}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B6%7D%7B20%7D%2A%5Cfrac%7B10%7D%7B19%7D)
![=\frac{3}{19}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%7D%7B19%7D)
Hence the probability that you first choose a green marble and then a blue marble is ![\frac{3}{19}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B19%7D)