The Probability of getting at least one head when tossing four fair coins is 15/16
Explanation:A coin as a head and a tail
Probability of getting a head = 1/2
Probability of getting a tail = 1 - 1/2 = 1/2
We need to find the probability of getting at least 1 head when tossing 4 coins.
To do this, we will apply the "at least once" rule
At least once rule states that:
[tex]\begin{gathered} Pr(at\text{ least 1head\rparen= 1 - \lparen Pr\lparen no head\rparen\rparen}^n \\ where\text{ n = number of times the fair coin was tossed} \end{gathered}[/tex][tex]\begin{gathered} Pr(no\text{ head\rparen = Pr\lparen tail\rparen = 1/2} \\ n\text{ = 4} \\ \\ Pr(at\text{ least 1 head\rparen = 1-\lparen}\frac{1}{2})^4 \\ Pr(at\text{ least 1 head\rparen= 1- }\frac{1}{2^4}\text{ = 1-}\frac{1}{16} \\ Pr(at\text{ least 1 head\rparen = }\frac{16-1}{16} \\ \\ Pr(at\text{ least 1 head\rparen =}\frac{15}{16} \end{gathered}[/tex]