Analysis and Approaches for IBDP Maths Ebook 1 | Page 260

Your Practice Set – Analysis and Approaches for IBDP Mathematics
85
Paper 1 Section B – Tree diagrams and
expected value of a distribution
Example
Petr travels to school on a train. On any day, the probability that Petr will miss the train is
0.2.
If he misses the train, the probability that he will be late for school is 0.9. If he does not
miss the train, the probability that he will be late is 0.25.
Let A be the event “he misses the train” and B the event “he is late for school”.
The information above is shown on the following tree diagram.
(a)
Find
(b)
(i) P( A� B)
;
(ii) P( B ) .
Find the probability that
[4]
(i)
Petr does not miss the train and is not late for school;
(ii)
Petr does not miss the train, given that he is late for school.
The cost for each day that Petr catches the train is 5 dollars. Petr goes to school on
Monday and Friday.
[5]
(c)
(d)
Copy and complete the probability distribution table.
X 0 5 10
P( X � x)
Find the expected cost for Petr for both days.
[3]
[2]
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