Final answer:
The statement 'The expected number of heads when flipping one of two coins, where one coin is fair and one is weighted so that P(H) = p' is true because it follows from the definition of expected value. Option a is correct.
Step-by-step explanation:
The question involves calculating the expected number of heads when flipping one of two coins, where one coin is fair and the other is weighted such that P(H)=p.
To calculate the expected number of heads, it's important to understand both the expected probability distributions for a fair coin and a biased coin. For a fair coin, the probability of getting heads, P(H), is 0.5. If we denote the probability of getting heads with the weighted coin as p, the combined expected number of heads after one flip of each would be 0.5 + p.
For example, if p = 0.75, which implies the weighted coin has a higher chance of landing on heads, the expected number of heads from flipping both coins once is (0.5 from the fair coin) + (0.75 from the weighted coin) = 1.25 heads. Note that we assume both coins are flipped independently.
Option a is correct.