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a. Find the probability the digital audio device works on the first try. (I wasn't sure if the pocket was a variable for solving (a.) But this is how I got this answer. (1/2) - 50% chance of choosing batteries from 2 pockets, added to (1/4 * 1/3) - choosing one out of four batteries and choosing one of three batteries.

b. Given that the digital audio device plays, calculate the prob. he chose two good batteries. (I thought that the first answer would be the 'given' for this question but it doesn't seem to be the case)

c. Given that the digital audio device plays, calculate the prob. he had placed all four batteries in the same pocket.