I'm in Biometrics, and I am having difficulty with the following question:

One classical experiment on ESP (extrasensory perception) tests for the ability of an individual to show telepathy-that is, to read the mind of another individual. This test uses five cards with different designs, all known to both participants. In a trial, the "sender" sees a randomly chosen card and concentrates on its design. The "receiver" attempts to guess the identity of the card. Each of the five cards is equally likely to be chosen, and only one card is the correct answer at any point.

a) Out of 10 trials, a receiver got four cards correct. What is her success rate? What is her expected rate of success, assuming she is only guessing?

For this, I said her success rate is 4/10, which is .4. For her expected success rate, I said that it is 1/5, which is .2. Am I wrong on the second part? I feel like I am.

b) Is her higher actual success rate reliable evidence that the receiver has telepathic abilities? Carry out the appropriate test.

For this, I'd assume to use the binomial test, using a probability of .2 (if I'm not wrong), and then do a test for Pr[4]+Pr[5]...+Pr[10].

I appreciate any assistance; I found Calculus 2 easier than statistics, and usually people say it's the other way around