Final answer:
The probability that at least one person out of 10 has type AB blood is calculated by subtracting the probability that none have type AB blood from 1. The chance that none have it is 0.8810, and the remaining difference is greater than 12%.
Step-by-step explanation:
To determine the probability that at least one out of 10 people will have type AB blood, we should first calculate the probability that none of the 10 people have type AB blood and then subtract that value from 1. Given that about 12% of the US population has type AB blood, the probability that a single individual does not have type AB blood is 88% or 0.88.
To find the probability that none of the 10 people have type AB blood, we raise 0.88 to the 10th power (0.8810). Subtracting this result from 1 gives us the probability that at least one person out of 10 has type AB blood. The calculation shows that this probability is greater than 12%, making option C the correct answer.
A person with type AB blood can donate red blood cells to people with the same blood type. Since about 12% of the US population has type AB blood, the probability that at least one person out of 10 will have type AB blood can be calculated using the complement rule. The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
Thus, the probability that none of the 10 people have type AB blood is 88% (1 - 0.12 = 0.88). Therefore, option B is correct. This means that the probability that at least one person has type AB blood is 12%, as stated in option A. Option C, which states that the probability of at least one person having type AB blood is greater than 12%, is incorrect. Option D, which states that the probability that all 10 people have type AB blood is 0%, is also correct.