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You flip a coin twice. $\newline$ What is the probability of getting tails and then getting heads? $\newline$ Simplify your answer and write it as a fraction or whole number. $\newline$ $\_\_\_\_$

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Probability of independent and dependent events

Full solution

Q. You flip a coin twice.

\newline

What is the probability of getting tails and then getting heads?

\newline

Simplify your answer and write it as a fraction or whole number.

\newline

\_\_\_\_

Sample Space: Understand the sample space for flipping a coin twice. $\newline$ When flipping a coin, there are two possible outcomes for each flip: heads (H) or tails (T). Therefore, when flipping a coin twice, the sample space consists of the following outcomes: $\{HH, HT, TH, TT\}$ .
Favorable Outcome: Identify the favorable outcome. $\newline$ The favorable outcome for this event is getting tails on the first flip and heads on the second flip, which is represented as $TH$ .
Calculate Probability: Calculate the probability of the favorable outcome. $\newline$ Since each flip is independent, the probability of getting tails on the first flip is $\frac{1}{2}$ , and the probability of getting heads on the second flip is also $\frac{1}{2}$ . To find the probability of both events happening in sequence, we multiply the probabilities of each event. $\newline$ Probability(TH) = Probability(T) $\times$ Probability(H) = $\left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right)$
Perform Multiplication: Perform the multiplication to find the probability. $\newline$ Probability( $TH$ ) = $(\frac{1}{2}) \times (\frac{1}{2}) = \frac{1}{4}$

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