Suppose that 60% of adults on PEI read The Guardian, 40% watch Computes, and 20%
ID: 3200094 • Letter: S
Question
Suppose that 60% of adults on PEI read The Guardian, 40% watch Computes, and 20% do both. (a) What is the probability that a randomly selected adult on PEI does not read The Guardian? (b) What is the probability that a randomly selected adult on PEI reads. The Guardian or watches Compass? (c) Given that an adult reads The Guardian, what is the probability that this person also watches Compass? (d) Are the events "read The Guardian" and "watches Compass" independent? (Explain your answer clearly using the mathematical definition of independence.)Explanation / Answer
P(reading The Guardian) = 0.6
P(watching Compass) = 0.4
P(reading The Guardian and watching Compass) = 0.2
a) P(not reading The Guardian) = 1 - P(reading The Guardian)
= 1 - 0.6
= 0.4
b) P(reading The Guardian or watching Compass) = P(reading The Guardian) + P(watching Compass) - P(reading The Guardian and watching Compass)
= 0.6 + 0.4 - 0.2
= 0.8
c) P(watching Compass | reading The Guardian) = P(watching Compass and reading The Guardian) / P(reading The Guardian)
= 0.2 / 0.6
= 0.33
d) P(reading The Guardian and watching Compass) = 0.2
P(reading The Guardian) * P(watching Compass) = 0.6 * 0.4 = 0.24
Since, P(reading The Guardian and watching Compass) is not equal to P(reading The Guardian) * P(watching Compass) , So the events are not independent.
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