After graduating from your university with a biology degree, you are interviewed for a lucrative job as a snake handler in a circus sideshow. As part of your audition, you must pick up two rattlesnakes from a pit. The pit contains eight snakes, three of which have been defanged and are assumed to be harmless, but the other five are definitely still dangerous. Unfortunately, budget cuts have eliminated the herpetology course from the curriculum, so you have no way of telling in advance which snakes are dangerous and which are not. You pick up one snake with your left hand and another snake with your right.

a. What is the probability that you picked up no dangerous snakes?

b. Assume that any dangerous snake you pick up has a probability of biting you. This probability is the same for each snake: 0.8. The defanged snakes do not bite. What is the chance that, in picking up your two snakes, you are bitten at least once?

c. Still assume that the defanged snakes do not bite and the dangerous snakes have a probability of 0.8 of biting. If you picked up only one snake and it did not bite you, what is the probability that this snake is defanged?