Given
A fair coin is flipped 3 times.
To find: What is the probability that the flips follow the exact sequence below?
Flip One: Heads
Flip Two: Heads
Flip Three: Tails
Explanation:
It is given that,
A fair coin is flipped 3 times.
Then, the sample space is,
[tex]\begin{gathered} S=\lbrace HHH,HHT,HTH,HTT,THH,TTH,THT,TTT\rbrace \\ n(S)=8 \end{gathered}[/tex]Let A be the event that the flips follow the sequence,
Flip One: Heads
Flip Two: Heads
Flip Three: Tails.
That implies,
[tex]\begin{gathered} A=\lbrace HHT\rbrace \\ n(A)=1 \end{gathered}[/tex]Therefore,
The probability that the flips follow the exact sequence is,
[tex]\begin{gathered} P(A)=\frac{n(A)}{n(S)} \\ =\frac{1}{8} \end{gathered}[/tex]Hence, the answer is 1/8.