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After graduating from your university with a degree in biology, you are interviewing 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 but the other five are definitely dangerous. Unfortunately, budget cuts have eliminated the herpetology course from the curriculum, so you have no way of knowing which snakes are safe and which are not. You pick up one snake with your right hand and another with your left.
a) What is the probability that you pick up no dangerous snakes?
b) Assume that any dangerous snake you pick up has a probability of 0.8 of biting you. The defanged snakes do not bite. What is the probability that you are bitten at least once?
c) Still assuming that the defanged snakes do not bite and dangerous snakes have a probability of 0.8 of biting you. If you pick up only one snake and it did not bite you, what is the probability that this snake is defanged?
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