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 tails.
the probability of getting zero tails is
(type an integer or a simplified fraction.)

Explanation:

Step1: Determine the number of favorable outcomes

The event of getting exactly zero tails means getting all heads. From the set \(\{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}\), the outcome with all heads is \(HHH\), so the number of favorable outcomes \(n = 1\).

Step2: Determine the total number of outcomes

The set of all possible outcomes has \(N=8\) elements.

Step3: Calculate the probability

The probability formula is \(P=\frac{n}{N}\). Substituting \(n = 1\) and \(N = 8\), we get \(P=\frac{1}{8}\).

Answer:

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