Question

maria plays basketball and is a 73% free throw shooter (meaning on average she hits 73 of 100 free throws). maria attempts seven free throw shots in a typical game. during a 25-game season, maria had a game in which she attempted seven free throws and hit all seven of them. do you think she had a \hot\ day, or was it just chance? explain your reasoning.

is the streak surprising? explain. select the correct choice below and fill in the answer box(es) within your choice.
(round to two decimal places as needed.)

a. the probability that she made seven free throw tosses out of seven is __, which is unlikely for any one game, but the probability of it happening at least once in the season is __, which is not surprising.
b. the probability that she made seven free throw tosses out of seven is ____, which is very unlikely regardless of the number of games in the season.
c. the probability that she made seven free throw tosses out of seven is __ and the probability of it happening at least once in the season is __ which makes it very surprising.
d. the probability that she made seven free throw tosses out of seven is ____, which is likely to happen regardless of the number of games in the season.

Explanation:

Calculate single game probability

We use the Probability concept.
The probability of making one free throw is \(p = 0.73\).
The probability of making seven out of seven in a single game is:

$$ P(\text{7 of 7}) = 0.73^7 \approx 0.1104 $$

This is approximately \(0.11\) or \(11.04\%\).

Calculate seasonal probability

We use the Probability concept.
The probability of not making seven out of seven in a single game is:

$$ 1 - 0.73^7 \approx 1 - 0.1104 = 0.8896 $$

For a 25-game season, the probability of this never happening is:

$$ (1 - 0.73^7)^{25} \approx 0.8896^{25} \approx 0.0537 $$

The probability of it happening at least once in the season is:

$$ 1 - (1 - 0.73^7)^{25} \approx 1 - 0.0537 = 0.9463 $$

This is approximately \(0.95\) or \(94.63\%\).

Evaluate the options

The single-game probability is \(0.11\), which is unlikely for any one game.
The seasonal probability is \(0.95\), which is highly likely.
Therefore, the streak is not surprising over a 25-game season.
This matches Option A.

Answer:

• (A) The probability that she made seven free throw tosses out of seven is 0.11, which is unlikely for any one game, but the probability of it happening at least once in the season is 0.95, which is not surprising. (Correct answer)
• (B) The probability that she made seven free throw tosses out of seven is 0.11, which is very unlikely regardless of the number of games in the season.
• (C) The probability that she made seven free throw tosses out of seven is 0.11 and the probability of it happening at least once in the season is 0.05, which makes it very surprising.
• (D) The probability that she made seven free throw tosses out of seven is 0.11, which is likely to happen regardless of the number of games in the season.