Question

The following table shows music preferences found by a survey of the faculty at a local university. Express your answers in fraction form.

a. Find the probability that a randomly selected person from this group likes co entry music.
b. What is the probability that a randomly selected person from this group likes rock music and is from the North?
c. Find the probability that a randomly selected person from this from this group likes oldies given that they are from the South.
d. Find P(R) in decimal form. Round to two decimal places.
e. Find P(S) in decimal form. Round to two decimal places.​

Answer 1

The probability values calculated from the two-way distribution table are :

• 0.260
• 0.035
• 0.47
• 0.44
• 0.53

From the table given :

1.) Probability that a randomly selected person likes country music

• P(country music) = 81 / 312 = 0.260

2. Probability of liking rock music and from the north :

• P(ROCK n North) = 11 / 312 = 0.035

3. Probability of liking oldies Given that person ls from the south :

• P(Oldies|South) = n(OnS) / n(S) = 44/93 = 0.47

4.)Probability of Rock music :

• P(R) = n(R) / n(Total) = 138/312 = 0.44

5.) Probability of person from South :

• P(S) = n(S) / n(Total) = 164 / 312 = 0.53

Therefore, the probability values can be calculated using values in the two way table.

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