2. John goes out for dinner every day. The probabilities he goes to restaurants

Question

2. John goes out for dinner every day. The probabilities he goes to restaurants A, B and C for dinner are 2, 10 and respectively. Ifhe goes to restaurant A, the probability ofordering dessert s 5 If he goes to restaurant B, the probability of ordering dessertis 3i and the probability of ordering 4 dessert isif he goes to restaurant C. 10 (a) Find the probability that John will order dessert today. (b) Given that John orders dessert today, find the probability that he goes to restaurant A today. (c) Find the probability that John will go to restaurant A for dinner but doesn't order dessert.

Explanation / Answer

a. By theorem of total probability,

P(Dessert) = P(Dessert | A)*P(A) + P(Dessert | B)*P(B) + P(Dessert | C)*P(C)

= (4/5)*(1/2) + (3/5)*(3/10) + (1/10)*(1/5)

= 0.60

b. P(A | Dessert) = P(Dessert | A)*P(A) / P(Dessert)

= (4/5)*(1/2) / 0.60

= 0.6667

c. P(No dessert | A) = 1 - P(Dessert | A) = 1 - (4/5)

= 1/5 = 0.20

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