To find the probability of drawing a ball numbered 6 on both the first and second draws from an urn containing balls numbered 1 through 10, we follow these steps:
-
Identify the Total Number of Outcomes: Since there are 10 balls, there are 10 possible outcomes for each draw.
-
Determine the Probability of Drawing a 6:
- The probability of drawing a ball numbered 6 in one draw is \( P(6) = \frac{1}{10} \).
-
Calculate the Probability for Two Independent Draws:
- Since the ball is returned to the urn after the first draw, the two draws are independent. Thus, the probability of both draws resulting in a 6 is the product of the probabilities of each individual draw: \[ P(\text{6 on 1st and 6 on 2nd}) = P(6) \times P(6) = \frac{1}{10} \times \frac{1}{10} = \frac{1}{100}. \]
Therefore, the probability that both the first and second balls will be a 6 is \(\frac{1}{100}\) or 0.01.