Question

Kay listens to either classical or country music every day while she works. If she listens to classical music one day, there is a 57% chance that she will listen to country music the next day. If she listens to country music, there is a 75% that she will listen to classical music the next day.

. All of the same information about Kay's listening habits remain true. However, suppose you know the additional fact that on a particular Monday the probability that she is listening to classical music is 0.2. (e) Based on your additional knowledge that there is a 0.2 probability that she is listening to classical music on Monday, what is the probability she will be listening to country music on Wednesday? (f) Based on your additional knowledge that there is a 0.2 probability that she is listening to classical music on Monday, what is the probability that she will be listening to classical music on Thursday?

Answer 1

Answer:

Probability of listening to classical music on one day given country music on the previous day = 0.75

So,Probability of listening to country music on one day given country music on the previous day = 1 - 0.75 = 0.25

Probability of listening to country music on one day given classical music on the previous day = 0.57

Probability of listening to classical music on one day given classical music on the previous day = 1 - 0.57 = 0.43

e) P(Classical on Monday) = 0.2

So, P(Country on Monday) = 1 - 0.2 = 0.8

P(Classical on Wednesday|Classical on Monday) = 0.6124 [ Part b) ]

So, P(Country on Wednesday|Classical on Monday) = 1 - 0.6124 = 0.3876

P(Classical on Wednesday|Country on Monday) = 0.51 [ Part a) ]

So, P(Country on Wednesday|Country on Monday) =1 - 0.51 = 0.49

So, P(Country on Wednesday) = P(Country on Wednesday|Classical on Monday) * P(Classical on Monday) + P(Country on Wednesday|Country on Monday) * P(Country on Monday)

= 0.3876 * 0.2+ 0.49 * 0.8

= 0.46952

f) P(Country music on Thursday|Classical music on Monday) = 0.445968 [ Part c) ]

So, P(Classical music on Thursday|Classical music on Monday) = 1 - 0.445968 = 0.554032

P(Country music on Thursday|Country music on Monday) = 0.4132 [ Part d) ]

So, P(Classical music on Thursday|Country music on Monday) = 1 - 0.4132 = 0.5868

P(Classical on Thursday) = P(Classical music on Thursday|Country music on Monday) * P(Country on Monday) + P(Classical music on Thursday|Classical music on Monday) * P(Classical on Monday)

= 0.5868 * 0.8 + 0.554032 * 0.2

= 0.5802464

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