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.
Solutions
2
3
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