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.
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.
Answers
GPT-4o mini
To find the simulation that best represents the basketball player's probability of making her free throws (75% success rate), we should look for a method that allows for approximately 75% of outcomes to represent a successful free throw.
1. **Rolling a six-sided die and counting outcomes of 1, 2, 3, or 4 as a made shot.**
- Probability of making a shot = 4 outcomes (1-4) out of 6 total outcomes = 4/6 = 66.67%. This simulates a lower probability than 75%.
2. **Flipping a coin, with heads representing a made shot.**
- Probability of making a shot = 1 out of 2 outcomes = 50%. This is also lower than 75%.
3. **Spinning a spinner divided into four equal sections and counting three of them as made shots.**
- Probability of making a shot = 3 outcomes (3 sections) out of 4 total outcomes = 3/4 = 75%. This matches the probability exactly.
4. **Drawing a card from a standard deck and counting red cards as made shots.**
- Probability of making a shot = 26 red cards out of 52 total cards = 26/52 = 50%. This is also lower than 75%.
Considering these options, the best simulation to represent the probability of the player making each free throw is:
**Spinning a spinner divided into four equal sections and counting three of them as made shots.**
1. **Rolling a six-sided die and counting outcomes of 1, 2, 3, or 4 as a made shot.**
- Probability of making a shot = 4 outcomes (1-4) out of 6 total outcomes = 4/6 = 66.67%. This simulates a lower probability than 75%.
2. **Flipping a coin, with heads representing a made shot.**
- Probability of making a shot = 1 out of 2 outcomes = 50%. This is also lower than 75%.
3. **Spinning a spinner divided into four equal sections and counting three of them as made shots.**
- Probability of making a shot = 3 outcomes (3 sections) out of 4 total outcomes = 3/4 = 75%. This matches the probability exactly.
4. **Drawing a card from a standard deck and counting red cards as made shots.**
- Probability of making a shot = 26 red cards out of 52 total cards = 26/52 = 50%. This is also lower than 75%.
Considering these options, the best simulation to represent the probability of the player making each free throw is:
**Spinning a spinner divided into four equal sections and counting three of them as made shots.**