Answer :
To solve this problem, we need to determine the number of possible outcomes when Sasha picks a ball three times, records the number, and returns the ball each time. Let's break this down step by step:
1. Total Number of Balls: There are 20 balls in the jar.
2. Number of Draws: Sasha picks a ball, records the number, and returns it to the jar. This process is repeated three times.
3. Outcomes for Each Draw: Since the ball is returned to the jar each time, each draw is independent. This means for each draw, Sasha has 20 possible outcomes (one for each ball).
4. Calculate Total Possible Outcomes:
- For the first draw, there are 20 possible numbers she could record.
- For the second draw, since the ball is put back, there are again 20 possible numbers she could record.
- For the third draw, once again, there are 20 possible numbers.
Since each draw is independent of the others, to find the total number of possible outcomes, we multiply the number of outcomes for each draw together:
[tex]\[ 20 \times 20 \times 20 = 20^3 \][/tex]
5. Result:
- [tex]\( 20^3 = 8000 \)[/tex]
Thus, the total number of possible outcomes when Sasha records three numbers, with each draw always having the ball replaced, is 8,000.
Therefore, the correct answer is:
d) 8,000
1. Total Number of Balls: There are 20 balls in the jar.
2. Number of Draws: Sasha picks a ball, records the number, and returns it to the jar. This process is repeated three times.
3. Outcomes for Each Draw: Since the ball is returned to the jar each time, each draw is independent. This means for each draw, Sasha has 20 possible outcomes (one for each ball).
4. Calculate Total Possible Outcomes:
- For the first draw, there are 20 possible numbers she could record.
- For the second draw, since the ball is put back, there are again 20 possible numbers she could record.
- For the third draw, once again, there are 20 possible numbers.
Since each draw is independent of the others, to find the total number of possible outcomes, we multiply the number of outcomes for each draw together:
[tex]\[ 20 \times 20 \times 20 = 20^3 \][/tex]
5. Result:
- [tex]\( 20^3 = 8000 \)[/tex]
Thus, the total number of possible outcomes when Sasha records three numbers, with each draw always having the ball replaced, is 8,000.
Therefore, the correct answer is:
d) 8,000
