Question

1. you throw a dart at the board shown. your dart is equally likely to hit any point insi the square board.

a. what is the probability your dart lands in the smallest triangle?
b. what is the probability your dart does not land anywhere in the circle?
the sections of a spinner are numbered 1 through 12. each section of the spinner ha the same area. you spin the spinner 180 times. the table shows the results. for whic number is the experimental probability of stopping on the number the same as the theoretical probability?
spinner results
1 2 3 4 5 6 7 8 9 10 11 12
13 21 22 20 11 8 14 9 15 12 18 17

Explanation:

Step1: Find theoretical probability

The spinner has 12 equal sections, so the theoretical probability of stopping on any number is $P_{theoretical}=\frac{1}{12}$. For 180 spins, the expected number of times (theoretical count) for each number is $180\times\frac{1}{12} = 15$.

Step2: Compare with experimental counts

We check the experimental results (the table values) to see which number has an experimental count equal to 15. Looking at the table:

• Number 1: 13
• Number 2: 21
• Number 3: 22
• Number 4: 20
• Number 5: 11
• Number 6: 8
• Number 7: 14
• Number 8: 9
• Number 9: 15
• Number 10: 12
• Number 11: 18
• Number 12: 17

The number 9 has an experimental count of 15, which matches the theoretical count. So the experimental probability for number 9 is $\frac{15}{180}=\frac{1}{12}$, same as theoretical.

Answer:

The number is 9 (or "Number 9" or "9" depending on how to present, but since the table has numbers 1 - 12, and the count for 9 is 15 which matches the theoretical count of 15 for 180 spins, the answer is 9).