An experiment is performec to flip a fair coin 10 times and

An experiment is performec to flip a fair coin 10 times and observe the outcome of each flip: heads (labeled \'H\') or tails (labeled \'T\'). For instance, one outcome, written as a 10-tuple, might be (H, T, T, T, T, T, T, H, H, H). How many total outcomes are there for this experiment? Explain your reasoning. How many ways can the result of the experiment show exactly nine tails? Explain your reasoning

Solution

1

a.

Each flip has two outcomes and total 10 flips. So total: 2^{10}=1024 outcomes

b.

Exactly nine tails is same as exactly one head. So choose one of the flips which is to be head/

This is done in: C(10,1)=10. So total outcomes.