Mathematics, 01.08.2019 06:40 pablohc200021

Abasketball player has a 50% chance of making each free throw. what is the probability that the player makes at least five out of six free throws?

Answers: 1

Show answers

Answers

For each free throw, there are only two possible outcomes, either the player makes it, or the player does not. The probability of the player making a free throw is independent of any other free throw, which means that the binomial distribution is used to solve this question.

Doing this, we get that: 0.1094 = 10.94% probability that the player makes at least five out of six free throws.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

--------------------------------------

A basketball player has a 50% chance of making each free throw

This means that p = 0.5

6 free throws:

This means that n = 6

--------------------------------------

What is the probability that the player makes at least five out of six free throws?

This is:

$P(X \geq 5) = P(X = 5) + P(X = 6)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{6,5}.(0.5)^{5}.(0.5)^{1} = 0.0938$

$P(X = 6) = C_{6,6}.(0.5)^{6}.(0.5)^{0} = 0.0156$

Then

$P(X \geq 5) = P(X = 5) + P(X = 6) = 0.0938 + 0.0156 = 0.1094$

Thus, 0.1094 = 10.94% probability that the player makes at least five out of six free throws.

A similar question is found at link

Answer from: 23jazzy

To start off, we want to figure this out by getting (the amount of possibilities of five or more free throws) divided by (the amount of possibilities total). To find the total amount of possibilities, we see that there are two possibilities for each throw, making a free throw or not. Next, we have another two for the next throw, and so on, resulting in 2*2*2*2*2*2=2^6=64 total possibilities. After that, we want to figure out the chance of making at least 5 shots, meaning that the player would either have to make 5 or 6 shots. To figure that out, we can use something called combinations, which states that we can choose r amount of things from n things. For the player to make 6 shots, we have C(6,6) or combination (6,6). To expand on that, the formula is
$\frac{n!}{r!(n-r)!} = \frac{6!}{6!(6-6)!} =$
Since 6!/6!=1 and 0!=1, or answer is 1 possibility, making the possibility of getting 6/6 shots is 1/64. For 5 shots, we get C(6,5)= $\frac{6!}{5!(6-5)!} =6$ because 6!=6*5*4*3*2*1, 5!=5*4*3*2*1 , and 1!=1. Therefore, the probability of getting 5 shots out of 6 is 6/64. Adding the probabilities of getting 5 or 6 shots together, we get 7/64 as the probability of getting at least 5 shots in.

Feel free to ask further questions!

Answer from: Quest

Ais the correct answer

Answer from: Quest

y-1700=200(x+4)

step-by-step explanation:

200(x+4) is 200x + 800 she is saving 200 per week x is the weeks and the -1700 is. us that’s howmuch she already had

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 15:00, kkqueen01

Ateacher has $80 to buy workbooks. each work book cost $3. if she buys as many workbooks as possible, how much money does she have leftover? a) $2 b) $4 c) $6 d) $8

Answers: 1

continue

Mathematics, 21.06.2019 22:30, malikvanison

Sum of the interior angles of a pentagon

Answers: 2

continue

Mathematics, 21.06.2019 23:00, janeou17xn

Mike wants to make meatloaf. his recipe uses a total of 8 pounds of meat. if he uses a 3 to 1 ratio of beef to pork, how much pork will he use? enter your answer as a mixed number in simplest terms.

Answers: 1

continue

Mathematics, 21.06.2019 23:40, afrimart1

Solve these problems: 1.what is the perimeter of an equilateral triangle with sides measuring 6cm? 2. a regular pentagon has sides measuring 3.2 cm. what is its perimeter? 3. a regular decagon has sides of 3.5mm . what is it’s perimeter? 4. a regular octagon has a perimeter of 64cm. what is the length of one of the sides? 5. a regular hexagon has a perimeter of 72mm . what is the length of one of the sides? 6. what is the perimeter of a rhombus with sides measuring 11m?

Answers: 2

continue

You know the right answer?

Abasketball player has a 50% chance of making each free throw. what is the probability that the play...