Questions: This question: 1 point(s) possible Submit quiz 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 H H, H T, T H, T T. Find the probability of getting the same outcome on each toss. A. 3/4 B. 1/4 C. 1/2 D. 1

Solution Steps

To find the probability of getting the same outcome on each toss, we need to identify the favorable outcomes and divide by the total number of possible outcomes. The favorable outcomes are those where both tosses result in the same side, which are "HH" and "TT". The total number of possible outcomes is 4.

When a fair coin is tossed two times, the set of equally likely outcomes is \(\{HH, HT, TH, TT\}\). Thus, the total number of possible outcomes is: \[ \text{Total Outcomes} = 4 \]

The favorable outcomes for getting the same result on both tosses are "HH" and "TT". Therefore, the number of favorable outcomes is: \[ \text{Favorable Outcomes} = 2 \]

The probability \(P\) of getting the same outcome on each toss is given by the ratio of favorable outcomes to total outcomes: \[ P = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{2}{4} = \frac{1}{2} \]

Final Answer