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You flip a coin twice.\newlineWhat is the probability of getting tails and then getting tails?\newlineSimplify your answer and write it as a fraction or whole number.\newline_____\_\_\_\_\_

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Full solution

Q. You flip a coin twice.\newlineWhat is the probability of getting tails and then getting tails?\newlineSimplify your answer and write it as a fraction or whole number.\newline_____\_\_\_\_\_
  1. Understand sample space: Understand the sample space for flipping a coin twice. 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}\{HH, HT, TH, TT\}.
  2. Identify favorable outcome: Identify the favorable outcome.\newlineThe favorable outcome for this event is getting tails on the first flip and tails on the second flip, which is represented as TTTT.
  3. Calculate probability: Calculate the probability of the favorable outcome.\newlineSince each flip of the coin is independent, the probability of getting tails on the first flip is 12\frac{1}{2}, and the probability of getting tails on the second flip is also 12\frac{1}{2}. To find the probability of both events happening, we multiply the probabilities of each event.\newlineProbability of TT = (Probability of T on first flip) ×\times (Probability of T on second flip) = (12)×(12)\left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right)
  4. Perform calculation: Perform the calculation.\newlineProbability of TT = (12)×(12)=14(\frac{1}{2}) \times (\frac{1}{2}) = \frac{1}{4}

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