Question

a fair coin is tossed 2 times in succession. the set of equally likely outcomes is {hh, ht, th, tt}. find the probability of getting a head on the first toss. the probability of getting a head on the first toss is (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the total number of outcomes

The set of outcomes is \(\{HH, HT, TH, TT\}\), so the total number of outcomes \(n(S)=4\).

Step2: Determine the number of favorable outcomes

The outcomes with a head on the first toss are \(\{HH, HT\}\), so the number of favorable outcomes \(n(E) = 2\).

Step3: Calculate the probability

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substituting the values, we get \(P(E)=\frac{2}{4}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)