Question

A box contains four red balls and eight black balls. Two balls are randomly chosen from the box, and are not replaced. Let event B be choosing a black ball first and event R be choosing a red ball second. What are the following probabilities?

Answer 1

To find the probability of event B (choosing a black ball first) and event R (choosing a red ball second), we can use the formula: P(B and R) = P(B) * P(R|B). Given that there are a total of 12 balls in the box (4 red and 8 black), the probability of choosing a black ball first is 2/3. After choosing a black ball, there are now 11 balls remaining in the box, with 3 red balls and 8 black balls. Therefore, the probability of choosing a red ball second, given that a black ball was chosen first, is 3/11. Plugging these values into the formula, we have P(B and R) = 2/11.

Step-by-step explanation:

To find the probability of event B (choosing a black ball first) and event R (choosing a red ball second), we can use the formula:

P(B and R) = P(B) * P(R|B)

Given that there are a total of 12 balls in the box (4 red and 8 black), the probability of choosing a black ball first is:

P(B) = 8/12 = 2/3

After choosing a black ball, there are now 11 balls remaining in the box, with 3 red balls and 8 black balls. Therefore, the probability of choosing a red ball second, given that a black ball was chosen first, is:

P(R|B) = 3/11

Plugging these values into the formula, we have:

P(B and R) = (2/3) * (3/11) = 2/11

Answer 2

First answer: 8/12
Second answer: 4/11
Third answer: 8/33
fourth answer: 24 percent