Question

Stats probability question

Assume the probability that a first-time tourist to Nashville will visit the Country Music Hall of Fame is 0.4, will visit The rmitage is 0.35, and will visit both is 0.2. Assume a first-time tourist to Nashville is randomly selected. Draw a Venn diagram for this situation a. Find the probability that the tourist will visit the Country Music Hall of Fame or The Hermitage b. Find the probability that the tourist will not visit The Country Music Hall of Fame. c. If a tourist visits the Country Music Hall of Fame, what is the probability he will visit The Hermitage? d. Based on these probabilities, are visiting the Country Music Hall of Fame and visiting The Hermitage independent events? Justify your answer e. Based on these probabilities, are visiting the Country Music Hall of Fame and visiting The Hermitage mutually exclusive events? Justify your answer: 5) What is the probability of obtaining a sum of 17 when three dice are tossed?

Answer 1

4)

P(hall of fame) = 0.4, P(Hermitage) = 0.35

P(hall of fame and Hermitage) = 0.2

a) P(hall of fame or Hermitage) = P(hall of fame) + P(Hermitage) - P(hall of fame and Hermitage)

= 0.4 + 0.35 - 0.2

= 0.55

b) P(no hall of fame) = 1 - P(hall of fame)

= 1 - 0.4

= 0.6

c) P(Hermitage / hall of fame)) = P(hall of fame and Hermitage) / P(hall of fame)

= 0.2/0.4

= 0.5

d) For hall of fame and Hermitage to be independent,

P(hall of fame and Hermitage) = P(hall of fame) * P(Hermitage)

Thus, 0.2 = 0.4*0.35

Thus, 0.2 = 0.14 which is not true and thus these are not independent events

e) P(hall of fame and Hermitage) = 0.2 and not 0 they are not mutually exclusive