A student flips a fair coin 6 times. Answer the following questions: 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? Suppose now that after each flip the experimenter records the result (i.e. HH or TT) of the flip. Find the number of outcomes in this sample space 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. HT B. HTHTHT C. HHTT D. THTHH E. HTHTHTH F. TTHTT G. TTH H. THH
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A student flips a fair coin 6 times. Answer the following questions:
- 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?
- Suppose now that after each flip the experimenter records the result (i.e. HH or TT) of the flip. Find the number of outcomes in this sample space
- 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. HT
B. HTHTHT
C. HHTT
D. THTHH
E. HTHTHTH
F. TTHTT
G. TTH
H. THH
Given Information:
A student flips a fair coin 6 times. Suppose that after flipping the coin all six times the experimenter noted the number of heads.
To find the total possible outcomes in the sample space.
The experimenter records the total number of heads after flipping the coin 6 times.
So, there are 7 possible outcomes in the sample space.
2) Suppose now that after each flip the experimenter records the result (i.e. H or T) of the flip.
If the experimenter records the result after each flip (H or T):
For the first slip, there are possibilities of getting two results (H or T), for the second flip, there are two possibilities (H or T), same for the third, fourth, fifth and sixth flip.
Thus, the possible outcomes in the sample space are:
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