(a) Describe in a sentence what each of the following probabilities represents: (i) P(B), (ii)P(L|B), (iii) P(B|Lc). (b) Compute P(L). Show your work. (c) Compute the probability that a student is in the band, given that they are in the play. Show your work

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Hello University has both a student concert band and a student play. Students at the school may be involved in both, neither, or exactly one of the two groups.
25% of the student body is in the band. If a student is in the band, then there is an 80% chance that they are in the play. If a student is not in the band, then there is a 10% chance that they are in the play.
Let B be the event that a student is in the band and L be the event that a student is in the play.

(a) Describe in a sentence what each of the following probabilities represents: (i) P(B), (ii)P(L|B), (iii) P(B|Lc).
(b) Compute P(L). Show your work.
(c) Compute the probability that a student is in the band, given that they are in the play. Show your work

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