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
(type an integer or a simplified fraction.)

Explanation:

Step1: Determine total outcomes

The set of outcomes has 8 elements: {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}, so total outcomes \( n = 8 \).

Step2: Identify favorable outcomes

Zero heads means all tails, which is TTT. So favorable outcomes \( m = 1 \).

Step3: Calculate probability

Probability formula: \( P = \frac{m}{n} \). Substitute \( m = 1 \), \( n = 8 \), so \( P = \frac{1}{8} \).

Answer:

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