Question
A basketball player makes 75% of her free throws. She is about to take four free throws in a row.
Which simulation would best represent the probability of her making each free throw?
(4 Points)
Rolling a six-sided die and counting outcomes of 1, 2, 3, or 4 as a made shot.
Flipping a coin, with heads representing a made shot.
Spinning a spinner divided into four equal sections and counting three of them as made shots.
Drawing a card from a standard deck and counting red cards as made shots.
25
(7.SP.C.7) A board game uses a spinner with three e
Which simulation would best represent the probability of her making each free throw?
(4 Points)
Rolling a six-sided die and counting outcomes of 1, 2, 3, or 4 as a made shot.
Flipping a coin, with heads representing a made shot.
Spinning a spinner divided into four equal sections and counting three of them as made shots.
Drawing a card from a standard deck and counting red cards as made shots.
25
(7.SP.C.7) A board game uses a spinner with three e
Answers
GPT-4o mini
To represent the probability of a basketball player making free throws, we want a simulation that accurately reflects her free throw success rate of 75%.
Let's evaluate the options:
1. **Rolling a six-sided die and counting outcomes of 1, 2, 3, or 4 as a made shot.**
- In this case, rolling a die has a 4 out of 6 chance to represent a made shot (1, 2, 3, or 4). This equates to a probability of \(\frac{4}{6} = \frac{2}{3} \approx 66.67\%\), which is lower than the 75%.
2. **Flipping a coin, with heads representing a made shot.**
- A coin flip gives a 50% chance for heads, which does not match the player's 75% make rate.
3. **Spinning a spinner divided into four equal sections and counting three of them as made shots.**
- This simulates a 75% probability because 3 out of 4 sections represent made shots. Each spin has a probability of \(\frac{3}{4} = 75\%\), which matches the player's success rate.
4. **Drawing a card from a standard deck and counting red cards as made shots.**
- A standard deck has 52 cards, 26 of which are red. This gives a probability of \(\frac{26}{52} = \frac{1}{2} = 50\%\), which is also less than 75%.
Given the evaluation of the simulations, the best representation of the basketball player's 75% free throw success rate is:
**Spinning a spinner divided into four equal sections and counting three of them as made shots.**
Let's evaluate the options:
1. **Rolling a six-sided die and counting outcomes of 1, 2, 3, or 4 as a made shot.**
- In this case, rolling a die has a 4 out of 6 chance to represent a made shot (1, 2, 3, or 4). This equates to a probability of \(\frac{4}{6} = \frac{2}{3} \approx 66.67\%\), which is lower than the 75%.
2. **Flipping a coin, with heads representing a made shot.**
- A coin flip gives a 50% chance for heads, which does not match the player's 75% make rate.
3. **Spinning a spinner divided into four equal sections and counting three of them as made shots.**
- This simulates a 75% probability because 3 out of 4 sections represent made shots. Each spin has a probability of \(\frac{3}{4} = 75\%\), which matches the player's success rate.
4. **Drawing a card from a standard deck and counting red cards as made shots.**
- A standard deck has 52 cards, 26 of which are red. This gives a probability of \(\frac{26}{52} = \frac{1}{2} = 50\%\), which is also less than 75%.
Given the evaluation of the simulations, the best representation of the basketball player's 75% free throw success rate is:
**Spinning a spinner divided into four equal sections and counting three of them as made shots.**