Knowee
Questions
Features
Study Tools

When shooting two free throws, the chance that a basketball player makes her first free throw is 70%. If she makes her first free throw, her confidence goes up and there is a 75% chance that she will make her second free throw. But, if she misses her first free throw, her confidence goes down and there is only a 50% chance that she will make her second free throw. Find the probability of each event below. Round each probability to four decimal places. You may find it useful to sketch yourself a tree diagram. (a) she makes both free throws? (b) she misses both free throws? (c) she makes exactly one of the two free throws? (d) she makes at least one of the free throws?

Question

When shooting two free throws, the chance that a basketball player makes her first free throw is 70%.

If she makes her first free throw, her confidence goes up and there is a 75% chance that she will make her second free throw. But, if she misses her first free throw, her confidence goes down and there is only a 50% chance that she will make her second free throw. Find the probability of each event below. Round each probability to four decimal places.

You may find it useful to sketch yourself a tree diagram.

(a) she makes both free throws?

(b) she misses both free throws?

(c) she makes exactly one of the two free throws?

(d) she makes at least one of the free throws?

...expand
🧐 Not the exact question you are looking for?Go ask a question

Solution

(a) The probability she makes both free throws:

First, we calculate the probability of her making the first free throw, which is 70% or 0.70. If she makes the first one, the probability of her making the second one is 75% or 0.75. The probability of both events happening is the product of their individual probabilities. So, 0.70 * 0.75 = 0.525 or 52.5%.

(b) The probability she misses both free throws:

The probability of her missing the first free throw is 30% or 0.30 (since the probability of her making it is 70%, the probability of her missing it is 100% - 70% = 30%). If she misses the first one, the probability of her missing the second one is 50% or 0.50. The probability of both events happening is the product of their individual probabilities. So, 0.30 * 0.50 = 0.15 or 15%.

(c) The probability she makes exactly one of the two free throws:

There are two scenarios here: she makes the first one and misses the second one, or she misses the first one and makes the second one.

For the first scenario, the probability is 0.70 (probability of making the first one) * 0.25 (probability of missing the second one, since if she makes the first one, the probability of her missing the second one is 100% - 75% = 25%) = 0.175 or 17.5%.

For the second scenario, the probability is 0.30 (probability of missing the first one) * 0.50 (probability of making the second one) = 0.15 or 15%.

The total probability is the sum of these two probabilities, so 0.175 + 0.15 = 0.325 or 32.5%.

(d) The probability she makes at least one of the free throws:

This is the complement of the event that she misses both free throws. So, the probability is 1 - the probability of her missing both free throws = 1 - 0.15 = 0.85 or 85%.

This problem has been solved

Similar Questions

When shooting two free throws, if a Red Devil basketball player makes her first free throw, there is a 90% chance that she will make her second free throw. If she misses her first free throw, there is only a 45% chance that she will make her second free throw. Suppose the chance she makes her first free throw is 70%, what is the probability: a) She makes both free throws? b) She misses both free throws? c) She makes exactly one of the two free throws? d) She makes at least one of the free throws? For each of the above, you may enter a calculation that leads to your answer.

Samantha makes 65% of all free throws she attempts. What is the probability she will miss her next shot?

A basketball player has a 25% accuracy rate at making three-point shots. Mark thought it was reasonable that each attempt was independent and the probability stayed at 25% for this player.Using the geometric distribution formula, what is the probability that the basketball player makes his first three-point shot on the third attempt? Answer choices are rounded to the hundredths place.a.)0.14b.)0.25c.)0.38d.)0.56

Carlos plays college soccer. He makes a goal 65% of the time he shoots. Carlos is going to attempt two goals in a row in the next game. A = the event Carlos is successful on his first attempt. P(A) = 0.65. B = the event Carlos is successful on his second attempt. P(B) = 0.65. Carlos tends to shoot in streaks. The probability that he makes the second goal given that he made the first goal P(B/A ) is 0.90. What is the probability that he makes both goals P (A and B)?

Minutes per Day Spent Practicing Free Throws and Percentage of Success for Five Basketball StudentsPlayer Minutes Practicing Free Throws Percentage of SuccessAdam 15 56%Jordan 30 74%Emma 45 78%Josie 60 62%A science class at a local high school conducted an experiment with their basketball team trying to determine a correlation between time spent practicing free throws and the percentage of free throws that went through the basket successfully. Four basketball players, Adam, Jordan, Emma and Josie, each spent a different amount of time per day practicing free throws for one week. At the end of the week, each player took 50 free throws and the science class recorded the percentage of success. They found that there was not a strong correlation between the amount of time spent practicing and the success rate. Thus, they claim that increasing practicing time doesn't necessarily improve the rate of success when it comes to free throws. Which choice best describes data from the table that supports the science class' claim?Adam's success rate was lower than Jordan's success rate. eliminateAdam's success rate was lower than Josie's success rate. eliminateJordan's success rate was lower than Emma's success rate.eliminateEmma and Jordan's success rates were roughly the same.

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.