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

Step-by-step 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 :

$P(B_1)=\dfrac{1}{40}=0.25\\\\P(B_2)=\dfrac{1}{2}=0.5\\\\P(B_3)=\dfrac{1}{4}=0.25$

Now, $P(G|B_1)=\dfrac{5}{10}=0.5$

$P(G|B_2)=\dfrac{3}{10}=0.3$

$P(G|B_1)=\dfrac{4}{10}=0.4$

By using the law of total probability, we have

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