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.