A player makes 42 out of 60 free throws. He is in a one on one situation.What is the probability he will score 0 points? 1 point? 2 points?
prob (hit) = 42/60 = 7/10
prob(miss) = 3/10
prob 0 points = 3/10 , (only gets one shot, a miss)
prob 1 point = (7/10)(3/10)
= 21/100 , (has to hit first, miss the second
prob 2 points = (7/1)(7/10) = 49/100
(has to make them both
did you notice that 3/10 + 21/100 + 49/100 = 100/100 = 1 ?
When you do a free throw, you get 2 tries
42/60=.7=7/10=70% probability(make)
10/10-7/10=3/10=30% probability (miss)
0 points= 3/10=30%
1 point= 7/10•3/10=21/100=21%
2 points= 7/10•7/10=49/100=49%
To make sure it's in the range of 100 as the whole number add 3/10+21/100+49/100=100/100
To calculate the probability, we first need to find the probability of making a free throw.
The player made 42 out of 60 free throws, so the probability of making a free throw is:
P(Making a free throw) = 42/60 = 0.7
Now, let's calculate the probability of scoring 0 points:
The player will score 0 points if he misses all the free throws. Since there are 60 throws and the probability of making a free throw is 0.7, the probability of missing a free throw is:
P(Missing a free throw) = 1 - P(Making a free throw) = 1 - 0.7 = 0.3
The player will need to miss all 60 free throws in order to score 0 points, so the probability of scoring 0 points is:
P(Scoring 0 points) = P(Missing a free throw)^60 = 0.3^60 ≈ 6.96e-27
Next, let's calculate the probability of scoring 1 point:
The player will score 1 point if he makes 1 free throw and misses the other 59 throws. Since there are 60 possible throws and the probability of making a free throw is 0.7, the probability of scoring 1 point is:
P(Scoring 1 point) = 60C1 * (0.7)^1 * (0.3)^59 ≈ 8.18e-25
Finally, let's calculate the probability of scoring 2 points:
The player will score 2 points if he makes 2 free throws and misses the other 58 throws. Since there are 60 possible throws and the probability of making a free throw is 0.7, the probability of scoring 2 points is:
P(Scoring 2 points) = 60C2 * (0.7)^2 * (0.3)^58 ≈ 2.08e-23
Therefore, the probabilities are approximately:
P(Scoring 0 points) ≈ 6.96e-27
P(Scoring 1 point) ≈ 8.18e-25
P(Scoring 2 points) ≈ 2.08e-23
To find the probability of scoring a certain number of points in a one-on-one situation, we need to know the player's shooting percentage. In this case, we know that the player made 42 out of 60 free throws.
To find the shooting percentage, we divide the number of made free throws by the total number of attempts. In this case, the shooting percentage would be 42/60, which simplifies to 0.7 or 70%.
Now, we can calculate the probability of scoring a certain number of points using the shooting percentage.
To find the probability of scoring 0 points:
The player would miss both of the free throws. Since the shooting percentage is 70%, the probability of missing a free throw is 1 - 0.7 = 0.3 or 30%. To get the probability of missing both free throws, we multiply 0.3 * 0.3 = 0.09 or 9%.
To find the probability of scoring 1 point:
The player would make one free throw and miss the other. Since the shooting percentage is 70%, the probability of making a free throw is 0.7. The probability of missing a free throw is 0.3. To get the probability of making one and missing one, we multiply 0.7 * 0.3 = 0.21 or 21%.
To find the probability of scoring 2 points:
The player would make both free throws. Since the shooting percentage is 70%, the probability of making a free throw is 0.7. To get the probability of making both free throws, we multiply 0.7 * 0.7 = 0.49 or 49%.
So, in a one-on-one situation, the probability of scoring 0 points is 9%, 1 point is 21%, and 2 points is 49%.