At least one head in three tosses

Text

A player tosses a coin $3$ times. What is the probability that a head comes up at least once?

Solution

It is convenient to switch to the complementary event «no heads», i.e. three tails in a row. The tosses are independent, so $P(\text{nessuna testa}) = \left(\frac{1}{2}\right)^3 = \frac{1}{8}.$ The probability of at least one head is the complement: $P(\text{almeno una testa}) = 1 - \frac{1}{8} = \boxed{\dfrac{7}{8}}$

Links

Topics: Probabilita
Concepts: Evento complementare
Methods: Complementare prob
Skills: Calcolo probabilita
Exercise type: Problema probabilita