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 \(P(E) = \frac{2}{4}\)
Other exercises in this chapter
Problem 19
The general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. $$a_{n}=\frac{n^{2}}{n !}$$
View solution Problem 20
Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (y-4)^{4} $$
View solution Problem 20
In Exercises \(11-30,\) use mathematical induction to prove that each statement is true for every positive integer \(n\) $$ \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+
View solution Problem 20
In Exercises \(17-20,\) does the problem involve permutations or combinations? Explain your answer. (It is not necessary to solve the problem. \()\) Fifty peopl
View solution