107. 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?
Answer: C
The probability that the outcomes of Mia's three coin tosses will include two heads and one tail is 38.
To calculate the probability of getting two heads and one tail in three coin tosses, we can use the binomial probability formula. The total number of outcomes for three tosses is 2^3, or 8, and the specific combinations yielding two heads and one tail amount to 3, making the probability 3/8, which corresponds to the option labeled as 38.
A) 18
This option is incorrect because the number 18 does not represent any probability outcome related to the scenario described. The correct approach involves calculating the specific combinations of heads and tails, which leads to a different result.
B) 28
Option B does not align with the coin toss probabilities. The number 28 does not represent the number of successful outcomes or the probability of obtaining two heads and one tail in three tosses, making it an invalid choice.
C) 38
This option is correct as it represents the probability of achieving two heads and one tail in Mia's three tosses. The calculation shows that there are three favorable outcomes (HHT, HTH, THH) out of a total of eight possible outcomes (2^3 = 8), leading to the correct answer.
D) 48
Option D is not correct as 48 does not correlate with the probabilities derived from the coin toss outcomes. The calculations show that there are not enough combinations to yield such a high probability value, thus making this choice invalid.
Conclusion
The correct answer is C) 38, as it accurately represents the probability of achieving two heads and one tail from three coin tosses. The other options fail to reflect the correct calculations and combinations associated with this probability scenario, confirming that option C is the only valid choice.