Let's first calculate the probability of picking two purple balls without replacement:
1. There is a total of 10 purple balls and 90 non-purple balls in the container. So, the probability of picking a purple ball on the first draw is 10/100 = 1/10.
2. Once you've picked a purple ball, there are now 9 purple balls left out of a total of 99 remaining balls. So, the probability of picking a purple ball on the second draw, given that you already picked a purple ball, is 9/99 = 1/11.
3. To find the probability of picking two purple balls without replacement, we multiply the probabilities from steps 1 and 2:
(1/10) * (1/11) = 1/110
Therefore, the probability of winning without replacement is 1/110.
Now, let's calculate the probability of picking two purple balls with replacement:
1. The probability of picking a purple ball on the first draw is still 1/10.
2. Since we are replacing the first ball, the probability of picking a purple ball on the second draw is still 1/10 since the probability of picking a purple ball does not change.
3. To find the probability of picking two purple balls with replacement, we multiply the probabilities from steps 1 and 2:
(1/10) * (1/10) = 1/100
Therefore, the probability of winning with replacement is 1/100.
To find the difference in probability between picking two purple balls with and without replacement, we subtract the probabilities:
1/100 - 1/110 = 11/1100 - 10/1100 = 1/1100
Therefore, if you are required to replace the first ball, the probability of winning is 1/1100 less likely compared to not replacing the first ball.
There is a large container which will hold the following:
The balls are all the same size and texture. You are required to select two balls.
If both of the balls that you select are purple then you win.
How much less likely are you to win if you are required to replace the first ball? Show all of your work and explain your steps.
Math
3 answers
can you explain the steps in a paragraph please
Sure! When selecting two purple balls without replacement, the probability of picking a purple ball decreases with each draw since there are fewer purple balls in the container. On the first draw, the chance of selecting a purple ball is 1/10. Then, after selecting a purple ball, there are 9 purple balls left out of a total of 99 remaining balls for the second draw, resulting in a probability of 1/11. Multiplying these probabilities, we get a chance of winning without replacement as 1/110. On the other hand, if you replace the first ball, the probability of picking a purple ball on the second draw remains at 1/10. The overall probability of winning with replacement is 1/100. The difference in probability between selecting two purple balls with and without replacement is 1/1100. Therefore, you would be 1/1100 less likely to win if you are required to replace the first ball.
1 answer