High School

The probability of choosing two green balls without replacement is [tex]\frac{11}{50}[/tex], and the probability of choosing one green ball is [tex]\frac{12}{25}[/tex]. What is the probability of drawing a second green ball, given that the first ball is green?

Answer :

Final answer:

The probability of drawing a second green ball given that the first ball drawn is green is calculated using conditional probability and is found to be 11/24. This requires knowing both the probability of drawing two green balls without replacement and the probability of drawing one green ball.

Explanation:

The student has asked about the probability of drawing a second green ball from a bag, given that the first ball drawn is green, without replacement. The probability of drawing one green ball is 12/25, and the probability of drawing two green balls, one after the other, without replacement, is 11/50.

To find the probability of drawing a second green ball after the first green has been drawn, we can use the conditional probability formula:

P(G₂|G₁) = P(G₁ and G₂) / P(G₁)

Where P(G₂|G₁) is the probability of drawing the second green ball given the first one is green, P(G₁ and G₂) is the probability of drawing both green balls, and P(G₁) is the probability of drawing the first green ball.

P(G₂|G₁) = (11/50) / (12/25) = (11/50) * (25/12) = 11/24.

Thus, the probability of drawing a second green ball given that the first ball drawn is green is 11/24.