Question

There are two boxes containing red and blue balls. For box A, there are 3red balls and 7blue balls. For box B, there are 6red balls and 4blue balls. Now randomly pick up one ball from the two boxes, and the selected ball is red. What is the probability that this red ball is from box A

Answer 1

0.3333 = 33.33% probability that this red ball is from box A.

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Red ball

Event B: From box A.

Probability of a red ball:

3/10 = 0.3 of 1/2 = 0.5(box A)

6/10 = 0.6 of 1/2 = 0.5(box B). So

`P(A) = 0.3*0.5 + 0.6*0.5 = 0.45`

Probability of a red ball from box A:

0.3 of 0.5, so:

`P(A \cap B) = 0.3*0.5 = 0.15`

What is the probability that this red ball is from box A?

`P(B|A) = (P(A \cap B))/(P(A)) = (0.15)/(0.45) = 0.3333`

0.3333 = 33.33% probability that this red ball is from box A.