José travels to school on a bus. On any day, the probability that José will miss

Question

José travels to school on a bus. On any day, the probability that José will miss the bus is If he misses his bus, the probability that he will be late for school is 8 If he does not miss his bus, the probability that he will be late is 8 Let E be the event "he misses his bus" and F the event "he is late for school" The information above is shown on the following tree diagram. (a) Find (i) P(En F) Find the probability that (i) (ii) (b) 3 José misses his bus and is not late for school; José missed his bus, given that he is late for school. Total (9 marks)

Explanation / Answer

a)(i) P(EnF) =P(E)*P(F|E) =(1/3)*(7/8) =7/24

(ii) P(F) =P(E)*P(F|E)+P(E')*P(F|E')=(1/3)*(7/8)+(2/3)*(3/8)=13/24

b)

(i)Jose miss the bus and not late =P(E nF')= P(E)**P(F'|E) =(2/3)*(5/8)=10/24 =5/12

(ii)Jose miss given late =P(E|F) =P(EnF)/P(F) =P(E)*P(F|E)/P(F) =(!/3)*(7/8)/(13/24) =7/13

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