The given game is fair, as both, you and your friend have equal probabilities of winning.
What is the probability of an event?
The probability of an event is the fractional value showing how likely an event is to occur. It is determined by the formula,
The probability of an event
= the number of outcomes favorable to the event/total number of outcomes.
How do we solve the given question?
All possible outcome when two coins are tossed is {HH, HT, TH, TT}
∴ The total number of outcomes = 4.
For you to win, we need both heads, that is {HH}.
∴ Number of outcomes in your favor = 1
Probability(you win) = 1/4
For a friend to win, we need both tails, that is {TT}.
∴ Number of outcomes in your friend's favor = 1
Probability(friend win) = 1/4
∵ Probability(you win) = Probability(friend win), we can say that the game is fair.
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