Question

Jamal gets ready for a basketball game by shooting \[10\] free-throws. Based on previous data, he has a \[70\%\] chance of making each free-throw. Assume that the results of each free-throw are independent. Which of the following would find the probability of Jamal making exactly \[8\] of \[10\] free-throws? Choose 1 answer: Choose 1 answer: (Choice A) \[\displaystyle{10 \choose 7}(0.70)^7(0.30)^3\] A \[\displaystyle{10 \choose 7}(0.70)^7(0.30)^3\] (Choice B) \[\displaystyle{10 \choose 8}(0.70)^8(0.30)^2\] B \[\displaystyle{10 \choose 8}(0.70)^8(0.30)^2\] (Choice C) \[\displaystyle{10 \choose 8}(0.70)^2(0.30)^8\] C \[\displaystyle{10 \choose 8}(0.70)^2(0.30)^8\] (Choice D) \[\displaystyle{70 \choose 10}(0.70)^8(0.30)^2\] D \[\displaystyle{70 \choose 10}(0.70)^8(0.30)^2\] (Choice E) \[(0.70)^8(0.30)^2\] E \[(0.70)^8(0.30)^2\]

Answer 1

The probability of Jamal making exactly 8 of 10 free-throws with a 70% success rate per throw is calculated with the binomial probability formula, represented by Choice B: <<10 choose 8>>(0.70)^8(0.30)^2.

Step-by-step explanation:

The student is asking about using the binomial probability formula to find the probability of Jamal making exactly 8 out of 10 free-throws, given that he has a 70% chance of making each throw and the throws are independent of each other.

The correct choice to find this probability is Choice B, which is <<10 choose 8>>(0.70)^8(0.30)^2. This formula reflects the binomial distribution, where 'n choose k' represents the number of ways to choose k successes out of n trials, p^k is the probability of success raised to the number of successes, and (1-p)^(n-k) is the probability of failure raised to the number of failures.

The probability of Jamal making exactly 8 of 10 free-throws can be found using the binomial probability formula. The formula is: {10 choose 8}(0.70)^8(0.30)^2. To explain this step by step, first, {10 choose 8} represents the number of ways to choose 8 free-throws out of 10. Next, (0.70)^8 represents the probability of making 8 free-throws, and (0.30)^2 represents the probability of missing 2 free-throws. Multiplying these three values together gives the probability of Jamal making exactly 8 free-throws.