Question

In: Statistics and Probability

In a debate program on TV, a specific theme is discussed. During the program, viewers have...

In a debate program on TV, a specific theme is discussed. During the program, viewers have the opportunity to send SMS and express their opinion on the topic. Suppose the viewer then answers yes or no to a question
related to the theme.
In this paper, we assume that 75% of viewers believe yes and 25% believe no (for simplicity, we assume that all viewers have an opinion on the question). We also assume that the probability that a random “yes-viewer” sends SMS is 0.01 and that the probability that a random “no-viewer” sends SMS is 0.05.
Let J be the event that a randomly selected viewer thinks yes, and let R be the event that a randomly selected viewer sends SMS.

a) Based on the information given above, write down what the probabilities are
P (J), P (J), P (R | J), and P (R | J)
becomes.
Draw a Friend Diagram illustrating the relationship between events J and R. Mark (event) the event R ∩ J in the diagram.
Show that P (R ∩ J) = 0.0075.

b) Find the probability of a random viewer sending SMS.
What percentage of those sending SMS to the debate program mean yes? That is, calculate P (J | R). Are the events R and J independent? Justify the answer.
Does the result of voting in the debate program give a correct picture of the viewer's perception of the question? Comment briefly.

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