Question

If you place the ball back into the hat, what is the probability that you pull out the 3 ball on your next draw?

A) 0.5 (either you draw a 3 or you don’t)
B) 1/10
C) 1/9
D) 0
E) 1

Answer 1

Each ball is equally likely, 1 desired out of 9 total = 1/9 and the correct option is C.

Here's why:

Option A (0.5) is incorrect because it doesn't consider the total number of balls. Even though there are only two possibilities (drawing a 3 or not), the probability of each outcome depends on the total number of balls in the hat.

Option B (1/10) is incorrect if there are more than 10 balls in the hat. With 10 balls, there would be a 10% chance of drawing the 3 balls, but the probability decreases as the total number of balls increases.

Option D (0) is incorrect because it's always possible to draw the 3 balls, regardless of how many other balls are in the hat.

Option E (1) is incorrect because it implies that you're guaranteed to draw the 3 ball, which isn't true.

Therefore, the correct answer is C) 1/9. This assumes there are 9 balls in the hat, including the one you put back in. Since there are 9 total possibilities (drawing any of the 9 balls), and only 1 of those possibilities is drawing the 3 balls, the probability is 1 out of 9, or 1/9.