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. There is only 1 outcome that is all heads (\(HHH\)).

Step2: Determine the total number of outcomes

The set of all possible outcomes is \(\{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}\), so there are \(n = 8\) total outcomes.

Step3: Calculate the probability

The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Substituting the values, we get \(P=\frac{1}{8}\).

Answer:

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