Probability and Combinatorics in Free Throws

The video tutorial explains how to calculate the probability of making a free throw, given a 70% success rate. It explores the probability of scoring exactly two times in six attempts using combinatorics and binomial coefficients. The tutorial provides examples and calculations to illustrate the process, concluding with a 6% probability of achieving exactly two scores in six attempts.

What is the probability of scoring a free throw if it is given as 70%?

• 0.5

• 1.0

• 0.7

• 0.3

If the probability of scoring is 0.7, what is the probability of missing a free throw?

• 0.5

• 1.0

• 0.7

• 0.3

In the context of six attempts, what are we trying to find the probability of?

• Exactly two scores

• Exactly two misses

• All misses

• All scores

What is the probability of making the first two free throws and missing the next four?

• 0.7^2 * 0.3^4

• 0.7^3 * 0.3^3

• 0.7^4 * 0.3^2

• 0.7 * 0.3^5

How many different ways can you achieve exactly two scores in six attempts?

• 20

• 25

• 15

• 10

What mathematical concept is used to determine the number of ways to achieve two scores in six attempts?

• Permutation

• Probability

• Combination

• Statistics

What is the formula for calculating combinations?

• n! / r!

• (n-r)! / n!

• n! / (r!(n-r)!)

• r! / n!

What is the overall probability of getting exactly two scores in six attempts?

• 0.25

• 0.105

• 0.059535

• 0.5

If the probability of scoring is high, is it likely to score only two times in six attempts?

• Impossible

• Equally likely

• No, unlikely

• Yes, very likely

What is the approximate percentage chance of scoring exactly two times in six attempts?

• 15%

• 10%

• 20%

• 6%