Question

Three boxes contain red and green balls. Box 1 has 5 red balls* and 5 green balls*, Box 2 has 7 red balls* and 3 green balls* and Box 3 contains 6 red balls* and 4 green balls*. The respective probabilities of choosing a box are 1/4, 1/2, 1/4. What is the probability that the ball chosen is green?

Answer 1

Answer: 0.375

Explanation:

Let G be the event that the chosen marble is green. Let
`B_i` be the event that we choose Box i.

The probabilities of choosing a box are :

`P(B_1)=(1)/(40)=0.25\\\\P(B_2)=(1)/(2)=0.5\\\\P(B_3)=(1)/(4)=0.25`

Now,
`P(G|B_1)=(5)/(10)=0.5`

`P(G|B_2)=(3)/(10)=0.3`

`P(G|B_1)=(4)/(10)=0.4`

By using the law of total probability, we have

`P(G)=P(G|B_1)P(B_1)+P(G|B_2)P(B_2)+P(G|B_3)P(B_3)\\\\\Rightarrow\ P(G)=0.25\cdot0.5+0.5\cdot0.3+0.25\cdot0.4=0.375`