An um contains balls numbered 1 through 10. A ball is chosen, returned to the urn, and a second ball is chosen. What is the probability that the first and second bails will be a 8?
Since the ball is returned to the urn after each selection, the probability of choosing an 8 on each draw is independent of the other.
The probability of choosing an 8 on the first draw is 1/10, since there is only 1 ball numbered 8 out of the total of 10 balls.
Similarly, the probability of choosing an 8 on the second draw is also 1/10, as the first ball chosen is returned to the urn and all the balls are put back in.
To find the probability of both events occurring, we multiply the probabilities together:
P(choosing an 8 on first draw and 8 on second draw) = P(choosing an 8 on first draw) * P(choosing an 8 on second draw)
= (1/10) * (1/10)
= 1/100
Therefore, the probability that both the first and second balls chosen are an 8 is 1/100 or 0.01.