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
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