Question

The probability that Rose will complete a free through basketball shot is 2/3. If she makes 5 shots,what is the probability of her completing at most 4 shots?

Answer 1

The probability of Rose completing at most 4 shots out of 5 is 361/243, which is approximately 1.48.

Step-by-step explanation:

To find the probability of Rose completing at most 4 shots out of 5, we need to find the sum of the probabilities of her making 0, 1, 2, 3, and 4 shots. The probability of her making a shot is 2/3, so the probability of her missing a shot is 1 - 2/3 = 1/3.

To calculate the probability of making a certain number of shots, we use the binomial probability formula. Let's calculate the probability for each scenario:

1. Probability of making 0 shots: (1/3)^5 = 1/243
2. Probability of making 1 shot: 5C1 * (2/3)^1 * (1/3)^4 = 5 * 2/3 * (1/3)^4 = 40/243
3. Probability of making 2 shots: 5C2 * (2/3)^2 * (1/3)^3 = 10 * 4/9 * (1/3)^3 = 80/243
4. Probability of making 3 shots: 5C3 * (2/3)^3 * (1/3)^2 = 10 * 8/27 * (1/3)^2 = 160/243
5. Probability of making 4 shots: 5C4 * (2/3)^4 * (1/3)^1 = 5 * 16/81 * (1/3) = 80/243

Now, we can sum up these probabilities:

Probability of at most 4 shots = (1/243) + (40/243) + (80/243) + (160/243) + (80/243) = 361/243 = 1.48