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Chapter 8: Problem 20

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.

Short Answer

Expert verified
The probability of getting the same outcome on each toss is \(0.5\) or \(50\%\)

Step by step solution

01

Identify all possible outcomes

Identify all the possible outcomes when a fair coin is tossed twice. The outcomes are: \(\{HH, HT, TH, TT\}\)
02

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 \(\{HH, TT\}\)
03

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 \(P(E) = \frac{2}{4}\)

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