Please provide answer and solution for number 13 and 14. Thanks! 13. [6 points]

Question

Please provide answer and solution for number 13 and 14. Thanks!
13. [6 points] Two fair dice (one red and one green) are rolled, and the numbers that face up are observed. Let A be the event that the red die is 1. Let B be the event that the sum of the numbers is either 3 or 4. Are A and B independent events? 14. [6 points] According to a study on the effect of music downloading on spending music 11% of all Internet users had decreased their spending on music, we estimate that 40% of all music fans used the Internet at the time of the study. If 20% of non-Internet users had decreased their spending on music, what percentage of those who had decreased their spending on music were internet users?

Explanation / Answer

Question 13:

P(A) = Probability that the red dice is a 3

P(A) = 1/ 6 as all faces are equally likely

P(B) = Probability that the sum is 3 or 4

Now the sum could be 3 or 4 in the following ways: (1red, 2green), (1red, 3 green), (2 red, 1 green), (2 red, 2 green), (3red, 1 green)

Therefore, there are 5 ways that we can get a sum of 3 or 4.

As there are 36 combinations possible for 2 dice throw, therefore the probability here would be computed as:

P(B) = 5/ 36

P(A and B) = this is only possible here is (1red, 2green), (1red, 3 green)

Therefore, P(A and B) = 2/36 = (1/18)

P(A)P(B) = (1/6)*(5/36) = (5/216) which is not equal to P(A and B)

Therefore A and B are not independent events.

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