A confused researcher finds a dime on the sidewalk and wants to test H0: p = 0.5 against HA: p ≠ 0.5 where p = Pr[Heads] when tossing the coin. This dime is an ordinary coin for which p = 0.5 -but she doesn't know that. She tosses the coin 100 times, finds the P-value for a goodness-of-fit test, and compares it to a = 0.05. However, if she retains H0 (because the P-value is large), then she discards the first sample and gets a new sample by tossing the coin 100 more times and repeating the goodness-of-fit test with the new data. If she retains //" for this test, then she discards the data and collects a third sample and does another goodness-of-fit test, after which she stops no matter what. What is the probability that she will make a type I error?