Mia will toss a fair coin three × and record whether the outcome is a head or a tail. A coin is fair if each time it is tossed, the coin lands either heads up or tails up, and the probability that the coin will land heads up is equal to the probability that the coin will land tails up. Which of the following is the probability that the outcomes of Mia's three coin tosses will include two heads and one tail?
The probability that the outcomes of Mia's three coin tosses will include two heads and one tail is 3/8.
To find the probability of getting exactly two heads and one tail in three tosses of a fair coin, we can use the binomial probability formula. The number of ways to arrange two heads and one tail is given by the combination formula, which results in 3 possible arrangements (HHT, HTH, THH). Each arrangement has a probability of (1/2) for heads and (1/2) for tails, leading to a total probability of 3/8.
This number does not represent a valid probability since probabilities range from 0 to 1. Therefore, 18 cannot correspond to the likelihood of a specific outcome occurring in this experiment.
Similar to choice A, 28 is outside the range of possible probabilities. Probabilities must be expressed as fractions or decimals between 0 and 1, so this choice is incorrect.
This choice is misleadingly formatted, but it could represent the correct probability of 3/8 when expressed in its simplest form. The correct interpretation aligns with the calculated probability for two heads and one tail.
This choice also fails to represent a legitimate probability value. As with the previous incorrect choices, 48 exceeds the maximum possible probability of 1 and cannot be accurate.
In conclusion, the calculation for the probability of obtaining exactly two heads and one tail from three tosses of a fair coin yields 3/8. The only valid probabilities must fall within the range of 0 to 1, and the incorrect options demonstrate values that cannot represent probabilities. Thus, the only reasonable interpretation of choice C aligns with this calculation, affirming the method used to determine the outcome.
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