Probability and statistics question

Question

In a given city, 60% of residents read the Morning Paper (event M) and 80% of them read the Evening Paper (event E). If 50% of residents read both Papers,

 

a. What is the probability that a randomly selected resident reads at least one Paper?

b. Given a randomly selected resident reads the Morning paper, what is the probability that s/he also reads the Evening Paper?

c. Are these events M and E statistically independent? Why?

d. If after two years P (M) = 0.51 and P (E) = 0.7 and P () = 0.357; can we conclude that these events are mutually exclusive? Why? Are they independent? Why?

Answer 1

all of these questions are applications of different probability rules!

For part (a) you can use the formula P(M u E) = P(M) + P(E) – P(both M and E)

So that ends up being 0.60 + 0.80 – 0.50 = 0.90 for this set of information

On part (b), it would be conditional probability

P(E/M) = P(M and E) / P(M)

So that ends up being 0.50 / 0.60 = 5/6

Part (c) is getting after independence. That can be checked by seeing if this formula holds

P(M and E) = P(M) * P(E)

for this set of data, 0.60*0.80 = 0.48, which does not equal 0.50, meaning that these events are not independent

Finally then for part (d), it’s a similar calculation just with updated values

0.51*0.80 = 0.357, which matches the overlap value. That means that in two years these events would be independent