Question

A student flips a fair coin 6 times. Answer the following questions: 1. Suppose that after flipping the coin all six times the experimenter noted the number of heads. How many outcomes are there in this sample space? 2. Suppose now that after each flip the experimenter records the result (.e. H or T) of the flip. Find the number of outcomes in this sample space. 3. Suppose now that the experimenter notes the result of each flip, but she will end the experiment early if she gets two heads or two tails in a row. She will still only flip a maximum of six times, however. Which of the following outcomes are possible in this experiment? A. TTHTT B. TTH Сc. HT D. HTHTHT E. HHTT F.HTHTHTH G. THTHH VH. THH

Answer 1

1. 7 outcomes.

2. 64 outcomes.

3. D and H

Explanation:

1. The experimenter will record the total number of heads after flipping the coin 6 times, therefore, the possible outcomes are: the experimenter got 0 heads, the experimenter got 1 head,..., the experimenter got 6 heads. Therefore there are 7 possible outcomes: (0, 1, 2, 3, 4, 5, 6).

2. If the experimenter records the result after each flip (H or T), for the first flip she has 2 results (heads or tails), for the second one she has 2 results, same for the third, fourth, fifth and sixth flip.

Therefore the possible outcomes are:
`(2)(2)(2)(2)(2)(2)=2^(6)=64`.

3. Now the experimenter will end up the experiment earlier if she gets two tails or two heads in a row.

A.TTHTT is not possible because in this case she would've ended up the experiment after the second flip since she got two tails.

B.TTH is not possible either for the same reason.

C. HT is not possible because she still needs to get another T or two H in a row.

D. This is a possible outcome because in this one she flipped the coin 6 times and she didn't get two heads or two tails in a row so she didn't finish it earlier.

E. Is not possible because she should've stopped after the second flip.

F. Is not possible because it has 7 letters, therefore, 7 flips.

G. Is not possible because she should've stopped once she got heads in the fourth and fifth flip.

H. Is possible because she got heads in the second and third flip.