A game consists of tossing a coin 3 times. Hanif wins if all the tosses give the same result. What is the probability that he loses the game?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{3}{4}\)
Three tosses of a coin have \(2\times2\times2=8\) equally likely outcomes. Hanif wins only when all three show the same face, so it is quicker to find his chance of winning and take it away from 1.
Winning outcomes: HHH and TTT, that is, 2 of the 8
P(win) \(\displaystyle=\frac{2}{8}=\frac{1}{4}\)
P(lose) \(\displaystyle=1-\frac{1}{4}=\frac{3}{4}\)