If you are required to replace the first ball, it means that after selecting the first ball, putting it back, and then selecting the second ball, you have the chance to select one of the purple balls again.
There are a total of 10 balls, and 2 of them are purple, so the probability of selecting a purple ball on the first draw is 2/10 or 1/5.
After replacing the first ball, the probability of selecting a purple ball on the second draw is again 2/10 or 1/5, because the odds do not change.
To calculate the probability of both events happening, you multiply the individual probabilities together:
P(selecting purple on first draw and purple on second draw) = P(purple on first draw) * P(purple on second draw)
= 1/5 * 1/5
= 1/25
Therefore, if you are required to replace the first ball, the probability of winning is 1/25 or 4%, which is less likely compared to not replacing the first ball where the probability was 1/20 or 5%.
The balls are all the same size and texture. You are required to select two balls. there are 10 balls, and two of those balls are purple.
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.
1 answer