One test for ESP involves using Zener cards. Each card shows one of five different symbols (square, circle, star, cross, wavy lines), and the person being tested has to predict the shape on each card before it is selected. Find each of the probabilities requested for a person who has no ESP and is just guessing.
a. What is the probability of correctly predicting 20 cards in a series of 100 trials?
b. What is the probability of correctly predicting more than 30 cards in a series of 100 trials?
c. What is the probability of correctly predicting 50 or more cards in a series of 200 trials?