Answer:
- <u>b) No it would not surprise you</u>
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
- Probability: 12 / 20 = 3/5
