## Solve Lesson 26 Page 43 Math Workbook 10 – Kite>

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:

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}\ )