At least one head in four tosses

Problem

A biased coin gives heads with probability $0,7$. Over $4$ tosses, what is the probability of getting at least one head?

Solution

It is convenient to switch to the complementary event «no head», that is four tails in a row. Tails has probability $1-0,7=0,3$ and the tosses are independent: $P(\text{nessuna testa}) = (0,3)^4 = 0,0081.$ Hence $P(\text{almeno una testa}) = 1 - (0,3)^4 = 1 - 0,0081 = \boxed{0,9919}$

Links

Topics: Probabilita
Concepts: Distribuzione binomiale · Evento complementare
Methods: Binomiale · Complementare prob
Skills: Calcolo probabilita
Exercise type: Problema probabilita