Problem 20

Question

A fair coin is tossed two times in succession. The sample space of equally- likely outcomes is \(\\{H H, H T, T H, T T\\} .\) Find the probability of getting: the same outcome on each toss.

Step-by-Step Solution

Verified
Answer
The probability of getting the same outcome on each toss is \(0.5\) or \(50\%\)
1Step 1: Identify all possible outcomes
Identify all the possible outcomes when a fair coin is tossed twice. The outcomes are: \(\{HH, HT, TH, TT\}\)
2Step 2: Identify favorable outcomes
Identify the outcomes that match the condition of 'getting the same outcome on each toss'. The outcomes favorable to the event are \(\{HH, TT\}\)
3Step 3: Calculate probability
Calculate the probability by taking the number of favorable outcomes and dividing by the total number of possible outcomes. The probability \(P(E)\) for an event \(E\) is given by \(P(E) = \frac{number of favorable outcomes}{total number of outcomes}\). In this case, it is \(P(E) = \frac{2}{4}\)