Question

We Built This Homework on Rock \& Roll The year is 1976 and The Rolling Stones and Fleetwood Mac are touring together. The Stones' line-up consists of Mick, Keith, Bill, Charlie, and Ronnie, while Fleetwood Mac consists of Mick, John, Christine, Lindsey, and Stevie. Note that there is a different Mick in each of the two bands (Jagger and Fleetwood, respectively). Each day on tour, one of the ten musicians is selected to select where everyone orders dinner from here. Suppose this selection is drawn from a uniform distribution (like picking names out of a hat).

(a)What is the probability that Keith is selected?
(b) What is the probability that Keith is selected given that the selected musician is from The Rolling Stones? Show how you could derive this using the probability formulas seen in class. Describe why this probability makes sense here, compared to your answer in (i).
(c) What is the probability that Keith is selected given that the selected musician is from Fleetwood Mac? Describe why this probability makes sense here, compared to your answer in (i).

Answer 1

The probability that Keith from The Rolling Stones is selected is 1/10. If we know the musician is from The Rolling Stones, this probability becomes 1/5. There is no chance of Keith being selected if we are only considering members of Fleetwood Mac.

Step-by-step explanation:

The question pertains to the field of probability and involves calculation of probabilities in specific contexts.

Calculating Probability

(a) Since there are 10 musicians and Keith is one among them, the probability that Keith is selected is 1/10 or 0.1, since each musician has an equally likely chance of being chosen.

(b) The probability that Keith is selected, given that the selected musician is from The Rolling Stones, uses the concept of conditional probability. Since there are 5 members in The Rolling Stones and Keith is one of them, the probability is 1/5 or 0.2. This makes sense as the sample space has now been reduced to the members of The Rolling Stones.

(c) The probability that Keith is selected given that the selected musician is from Fleetwood Mac is 0, because Keith is not a member of Fleetwood Mac. This question illustrates the concept of impossible events in probability. Since the event of selecting Keith from Fleetwood Mac cannot occur, the probability is 0.