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You flip a coin twice.\newlineWhat is the probability of getting tails and then getting heads?\newlineWrite your answer as a percentage.\newline____%\_\_\_\_\%

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Full solution

Q. You flip a coin twice.\newlineWhat is the probability of getting tails and then getting heads?\newlineWrite your answer as a percentage.\newline____%\_\_\_\_\%
  1. Coin Flip Probability: The possible outcomes when flipping a coin are {Heads,Tails}\{\text{Heads}, \text{Tails}\}. The probability of getting tails on the first flip is P(Tails on first flip)=Favorable outcomesTotal outcomes=12P(\text{Tails on first flip}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{1}{2}
  2. First Flip: Tails: Similarly, the probability of getting heads on the second flip is also P(Heads on second flip)=Favorable outcomesTotal outcomes=12P(\text{Heads on second flip}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{1}{2}
  3. Second Flip: Heads: The probability of two independent events both occurring is the product of their individual probabilities. Therefore, the probability of getting tails on the first flip and heads on the second flip is P(Tails then Heads)=P(Tails on first flip)×P(Heads on second flip)=12×12=14P(\text{Tails then Heads}) = P(\text{Tails on first flip}) \times P(\text{Heads on second flip}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
  4. Combined Probability: To express the probability as a percentage, we multiply the probability by 100100. So, P(Tails then Heads)P(\text{Tails then Heads}) as a percentage is (14×100)%=25%(\frac{1}{4} \times 100)\% = 25\%

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