The game is fair because there is an equal chance of winning an losing the game.
What is probability?
Probability is simply how likely something is to happen.
Probability formula
[tex]P(E )=\frac{Number\ of \ favorable\ outcomes }{Total\ number \ of outcomes}[/tex]
Where,
P(E) is the probability of an event.
What is the fair game?
A fair game is the game in which there is an equal chance of wining or losing.
According to the given question.
Two coins are tossed.
[tex]\implies sample\ space= \{ HH, HT, TH, TT\}[/tex]
[tex]\implies total\ number \ of outcomes = 4[/tex]
Therefore,
The probability that you win is given by
[tex]P(E_{1} )=\frac{Number\ of \ favorable\ outcomes }{Total\ number \ of outcomes}[/tex]
[tex]\implies P(E_{1} )= \frac{1}{4}[/tex] (getting HH is a favorable outcome)
[tex]\implies probability\ of\ losing\ the\ game = 1-\frac{1}{4} =\frac{3}{4}[/tex]
And, the probability that your friend wins the game is given by
[tex]P(E_{2}) = \frac{Total\ number\ of\ favorable\ outcomes\ }{Total\ number\ of\ outcomes}[/tex]
[tex]\implies P(E_{2} )=\frac{1}{4}[/tex] (getting TT is the favorable outcome)
[tex]\implies probability\ of\ losing\ the\ game = 1-\frac{1}{4} =\frac{3}{4}[/tex]
Hence, the game is fair because there is an equal chance of winning an losing the game.
Find out more information about probability and fair game here:
https://brainly.com/question/22582276
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