Question

use the theoretical probability formula to solve the problem. express the probability as a fraction reduced to lowest terms. a fair coin is tossed two times in succession. the set of equally likely outcomes is {hh, ht, th, tt}. find the probability of getting the same outcome on each toss. a. 1/4 b. 3/4 c. 1/1 d. 1/2

Explanation:

Step1: Identify total outcomes

The sample - space when a coin is tossed twice is $\{HH, HT, TH, TT\}$, so the total number of equally - likely outcomes $n(S)=4$.

Step2: Identify favorable outcomes

The favorable outcomes (getting the same outcome on each toss) are $\{HH, TT\}$, so the number of favorable outcomes $n(E) = 2$.

Step3: Calculate probability

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

Answer:

$\frac{1}{2}$