Topic
Toss a coin 3 times in a row
a) Find the number of elements of the set \(\Omega \) which is the sample space in the above game
b) Identify each event:
A: “Second appearance of heads”
B: “Tails appear exactly twice”
Solution method – See details
The probability of event A being a number, symbol \(P\left( A \right)\) is determined by the formula: \(P\left( A \right) = \frac{{n\left( A \right)}}{{n\left( \Omega \right)}}\), where \(n\left( A \right)\) and \(n\left( \Omega \right)\) denote the number of elements of set A and \(\Omega \) respectively.
Detailed explanation
a) Toss a coin 3 times in a row \( \Rightarrow n\left( \Omega \right) = 2.2.2 = 8\)
b) Identify each event:
A: “Second heads appear” \(A = \left\{ {NNN;NNS;SNN;SNS} \right\}\)\( \Rightarrow n\left( A \right) = 4\)
\( \Rightarrow P\left( A \right) = \frac{{n\left( A \right)}}{{n\left( \Omega \right)}} = \frac{4}{8} = \frac{1}{2}\)
B: “Heads up twice” \(B = \left\{ {NSS;SNS;SSN} \right\}\)\( \Rightarrow n\left( B \right) = 3\)
\( \Rightarrow P\left( B \right) = \frac{{n\left( B \right)}}{{n\left( \Omega \right)}} = \frac{3}{8}\ )
