Thank you so much!!
Nicky is a 60% free-throw shooter in a two-shot free-throw situation. Is she likely to score 0 points, 1 point, or 2 points?
can you please explain to me how to get the answer.
Assuming each shot is an independent event..
Pr(0)=.4*.4
Pr (1)=2*.6*.4
Pr (2)= .6*.6
Those are the probablities. The reason for the 2 in the second one is there is two ways to score one point, make it on the first, or make it on the second. She is most likely to score one point.
To determine whether Nicky is likely to score 0, 1, or 2 points in a two-shot free-throw situation, we can use probability calculations. In this case, we need to assume that each shot is an independent event, meaning the outcome of one shot does not affect the outcome of the other shot.
Let's break down the probabilities:
1. Probability of scoring 0 points (missing both shots): To find this, we multiply the probability of missing the first shot (0.4) by the probability of missing the second shot (also 0.4). Mathematically, Pr(0) = 0.4 * 0.4 = 0.16, which means there is a 16% chance of scoring 0 points.
2. Probability of scoring 1 point: There are two ways to score exactly 1 point in a two-shot situation. First, Nicky could make the first shot (probability of making it = 0.6) and miss the second shot (probability of missing it = 0.4). Second, Nicky could miss the first shot (probability of missing it = 0.4) and make the second shot (probability of making it = 0.6). To find the total probability of scoring 1 point, we multiply these two options by 2 because either scenario can happen. Mathematically, Pr(1) = 2 * 0.6 * 0.4 = 0.48, which means there is a 48% chance of scoring 1 point.
3. Probability of scoring 2 points (making both shots): To find this, we multiply the probability of making the first shot (0.6) by the probability of making the second shot (also 0.6). Mathematically, Pr(2) = 0.6 * 0.6 = 0.36, which means there is a 36% chance of scoring 2 points.
Based on these calculations, the probabilities are as follows:
- Probability of scoring 0 points is 16%
- Probability of scoring 1 point is 48%
- Probability of scoring 2 points is 36%
Therefore, Nicky is most likely to score 1 point in a two-shot free-throw situation.
To determine the likelihood of Nicky scoring 0, 1, or 2 points, we can use probability calculations based on her shooting percentage.
Assuming each shot is an independent event, the probability of scoring 0 points is calculated by multiplying the probability of missing the first shot (0.4) by the probability of missing the second shot (also 0.4). This gives us:
Pr(0) = 0.4 * 0.4 = 0.16
Next, we calculate the probability of scoring 1 point. Since there are two ways to score just one point (make the first shot and miss the second, or miss the first shot and make the second), we multiply the probability of making a shot (0.6) by the probability of missing a shot (0.4), and then multiply that by 2. This gives us:
Pr(1) = 2 * 0.6 * 0.4 = 0.48
Finally, we calculate the probability of scoring 2 points, which is the probability of making both shots. This is simply the product of the probability of making a shot twice:
Pr(2) = 0.6 * 0.6 = 0.36
Based on these calculations, we can see that Nicky is most likely to score 1 point, as the probability of this outcome (0.48) is higher than the probabilities of scoring 0 points (0.16) or 2 points (0.36).