Question

Each of the 20 students in Mr. Anderson's class flipped a coin ten times and recorded

how many times it came out heads.
a. How many heads do you think you will see out of ten tosses?
b. Would it surprise you to see 4 heads out of ten tosses? Explain why or why not.
c. Here are the results for the twenty students in Mr. Anderson's class. Use this data to
estimate the probability of observing 4, 5 or 6 heads in ten tosses of the coin. (It might
help to organize the data in a table or in a dot plot first.)
Student
1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16
18
19
20
Number of heads
3 5 4 6 4 8 5 4 9 S
3
58 6
6 5
Hint: PART A- WHAT IS THE ACTUAL PROBABILITY OF FLIPPING HEADS?
Hint: PART C- Count the number of students that got heads 4, 5 or 6 times? What is the probability? Remember there are 20 students!​

Answer 1

• a) 5

• b) No it would not surprise you

• c) 3/5

Step-by-step explanation:

a. The theoretical probability of flipping heads when a coin is tossed is 1/2 = 0.5.

Then, out of ten tosses you sould expect an average (mean) fo 0.5 × 10 = 5 heads.

The actual probability is the experimental probability, which is determined with the results for the twenty students.

The data shown in the questions are wrong and incomplete.

The correct data for this question, found in the internet are:

Student Number of heads

1 3

2 5

3 4

4 6

5 4

6 8

7 5

8 4

9 9

10 5

11 3

12 4

13 7

14 5

15 8

16 6

17 3

18 6

19 5

20 7

Then, the experimental or actual probability may differ from the theoretical probability.

The experimental probability is calculated as the number of times an outcome is observed divided by the number of times the experiment was performed.

The number of heads was:

3 + 5 + 4 + 6 + 4 + 8 + 5 + 4 + 9 + 5 + 3 + 4 + 7 + 5 + 8 + 6 + 3 + 6 + 5 + 7 = 107

Then, 107 / (200) = 0.535 is the actual probability.

It is close, but not exactly the same as, the theoretical probability.

b. Nevertheless, that is just a probability, it is not a certain value. It should not be surprising that instead of 5 heads and 5 tails, you see 4 heads and 6 tails out of ten tosses.

If you toss the coin 100 times (instead of 10) it would be suprising to see 40 heads and 60 tails, because as the number of trials increases, by the law of large numbers, the average should be closer to expected value.

c. The probability of getting heads 4, 5 or 6 times is:

• Number of students that got heads 4 times: 4
• Number of students that got heads 5 times: 5
• Number of students that got heads 6 times: 3

Total: 12

• Number of students: 20

• Probability: 12 / 20 = 3/5