Question 10

Explanation

Calculating Total Balls

The bag contains $4$ green balls and $5$ black balls.

Probability of First Green Ball

The probability of drawing a green ball on the first draw is the number of green balls divided by the total number of balls.

Probability of Second Green Ball

Since the draw is without replacement, the number of green balls decreases to $3$ and the total number of balls decreases to $8$.

Calculating Total Probability

The probability that both balls are green is the product of these two probabilities:

Thus, the probability that both balls are green is $\frac{1}{6}$.