Question

. Alice and Mary practice free throws at the basketball court after school.Alice makes free throws with probability and Mary makes them with probability Find the probability of the following outcomes when Alice and Mary each take one shot: Alice scores a basket; Either Alice or Mary scores a basket; both score; both miss

Answer 1

Using probability concepts, and supposing a probability of 0.7 for Alice and 0.6 for Mary, it is found that there is a:

• 0.7 = 70% probability that Alice scores a basket.

• 0.88 = 88% probability that either Alice of Mary scores a basket.

• 0.12 = 12% probability of both missing.

• 0.42 = 42% probability that both score.

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

• If two events are independent, the probability of both happening is the multiplication of the probabilities of each, that is: $P(A \cap B) = P(A)P(B)$

• To solve this question, we suppose that Alice has a 0.7 probability of making it and Mary a 0.6 probability.

• From the probabilities, there is a 0.7 = 70% probability that Alice scores a basket.

• Alice has a probability of 1 - 0.7 = 0.3 of missing, Mary 0.6, as 1 - 0.4 = 0.6, thus, the probability of both missing is:

$p = 0.3(0.4) = 0.12$

0.12 = 12% probability that both miss.

• Either is the complement of both missing, thus there is a 1 - 0.12 = 0.88 = 88% probability that either Alice of Mary scores a basket.

• Alice has a 0.7 probability of scoring, Mary 0.6, thus, the probability that both score is:

$p = 0.7(0.6) = 0.42$

0.42 = 42% probability that both score.

A similar problem is given at https://brainly.com/question/24935451