A scientist studying crabs has 5 different species (labeled 1 through 5), with the following probabilities of finding them in a cave:

Label Probability

1 25%

2 5%

3 20%

4 35%

5 15%

(a) What is the probability of incorrectly labeling a crab if the scientist predicts the species uniformly at random?

(b) Can the scientist improve his error by picking the same label every time? If so, what label should the scientist choose and what would the probability of being incorrect be?