For the following unrelated parts, consider this condition: Jake inadvertently mixed up five new batteries as well as three dead batteries in a drawer. When you're asked to find out a probability, compute it to 5 decimal places.
a) If Jake randomly chooses one battery from the eight batteries, determine the probability that it is a dead battery?
b) If the eight batteries are all distinguishable, in how many different manners can Jake put one battery in flashlight, four batteries in a radio, and three batteries in a camera?
c) If Jake randomly chooses four batteries from the eight batteries to install in radio and radio works only if none of the batteries are dead, determine the probability the radio works? You should employ a sample space of combinations.
d) If Jake randomly chooses a battery from eight batteries and puts it in toy pink bunny and then randomly chooses another battery from the remaining batteries as well as puts it in second toy pink bunny, determine the probability that both bunnies operate? You should use the multiplication rule that involves conditional probability.
e) Jake randomly chooses a battery from the eight batteries for his flashlight, but is interrupted by phone call. While answering the call, his wife returns battery to the drawer. After hanging up, Jake again randomly chooses a battery for his flashlight. Determine the probability that at least one of his two selections results in dead battery?