Question

8. I have a nephew Berkeley and niece Chelsea (true) who, when very young, would occasionally visit their Uncle Ismor on weekends (also true). Furthermore, i. Berkeley and Chelsea visited independently of one another. ii. Berkeley visited with probability 80%. iii. Chelsea visited with probability 75%. However, it often happened that some object in his house – especially if it was fragile – accidentally broke during such visits (not true). Furthermore, iv. The probability of such an accident occurring, given that both children visited, was 90%. V. The probability of such an accident occurring, given that only Berkeley visited, was 35%. vi. The probability of such an accident occurring, given that only Chelsea visited, was 20%. vii. The probability of such an accident occurring, given that neither child visited, was 2%. Sketch and label a Venn diagram for events A = Accident, B = Berkeley visited, and C = Chelsea visited. (Hint: The Exercise on page 3.2-3 might be useful.)

Answer 1

Probability that both B and C visit = 0.8*0.75 (since they are independent) = 0.6

Probability of accident when both visit = 0.6*0.9 = 0.54

P(A and B) = 0.35*0.8 = 0.28 (accident when only B visits)

P(A and C) = 0.2*0.75 = 0.15 (accident when only C visits)

Accident when nobody visits = 0.2

So the Venn diagram is as follows:

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