Question

a fair coin is tossed three times in succession. the set of equally likely outcomes is {hhh, hht, hth, thh, htt, tht, tth, ttt}. find the probability of getting exactly zero heads. the probability of getting zero heads is \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the total number of outcomes

When a coin is tossed \(n = 3\) times, the total number of outcomes \(N\) is \(2\times2\times2=2^{3}=8\) (since each toss has 2 possible outcomes - head or tail).

Step2: Determine the number of favorable outcomes

The event of getting zero heads means getting all tails. There is only 1 outcome that is all - tails (\(TTT\)). Let the number of favorable outcomes be \(M = 1\).

Step3: Calculate the probability

The probability \(P\) of an event is given by the formula \(P=\frac{M}{N}\). Substituting \(M = 1\) and \(N = 8\), we get \(P=\frac{1}{8}\).

Answer:

\(\frac{1}{8}\)