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You flip a coin twice. $\newline$ What is the probability of getting tails and then getting tails? $\newline$ Write your answer as a percentage. $\newline$ $\_\_\_\_\%$

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Probability of independent and dependent events

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Q. You flip a coin twice.

\newline

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

\newline

Write your answer as a percentage.

\newline

\_\_\_\_\%

Coin Flip Probability: The possible outcomes when flipping a coin are \{Heads, Tails\}. The probability of getting tails on a single flip is $P(\text{Tails}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{1}{2}$
Independent Events: Since the flips are independent events, the probability of getting tails on the first flip and tails on the second flip is the product of their individual probabilities. Therefore, P(\text{Tails and then Tails}) = P(\text{Tails on first flip}) \times P(\text{Tails on second flip}) \(\newline= \frac{1}{2} \times \frac{1}{2} $\newline$ = \frac{1}{4}\)
Percentage Conversion: The probability as a fraction is $\frac{1}{4}$ . To convert this probability to a percentage, we multiply by $100$ . $\newline$ $(\frac{1}{4}) \times 100 = 25\%$

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