1a An experiment is performed to flip a fair coin 10 times a

1a. An experiment is performed 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).

a. How many total outcomes are there for this experiment? Explain your reasoning.

b. How many ways can the result of the experiment show exactly nine tails? Explain your reasoning.

Solution

a)

A coin consist of 2 sides head and tails and this is flipped for 10 times

so it is

2¹⁰ =1024 outcomes

b)

as there are asked for exactly 9 tails...i.e., a minimum of 9 tails

in this case there is only one place for head out of 10 flips and can be taken as 10C₁ ways = 10 ways

another possibility is all tails in this also there are 9 tails so 10C₁₀ = 1 way

So total is

10+1 = 11 ways

11 ways since they can be all truth and as shown below…

(T,T,T,T,T,T,T,T,T,T), (H,T,T,T,T,T,T,T,T,T),

(T,H,T,T,T,T,T,T,T,T), (T,T,H,T,T,T,T,T,T,T),

(T,T,T,H,T,T,T,T,T,T), (T,T,T,T,H,T,T,T,T,T),

(T,T,T,T,T,H,T,T,T,T), (T,T,T,T,T,T,H,T,T,T),

(T,T,T,T,T,T,T,H,T,T), (T,T,T,T,T,T,T,T,H,T),

(T,T,T,T,T,T,T,T,T,H).