Apps. and Interpretation for IBDP Maths Ebook 1 | Page 285

2. Sandy and Katie both wish to go to the shopping mall but one of them has to stay home
for baby-sitting. The probability that Sandy goes to the shopping mall is 0.2. Exactly one
of them will go. If Sandy goes to the shopping mall the probability that she is late back
home is 0.7. If Katie goes to the shopping mall the probability that she is late back home
is 0.4.
Let S be the event that Sandy goes to the shopping mall, and L be the event that the
person who goes to the shopping mall arrives home late. The information above is shown
on the following tree diagram.
(a)
Find
(i) P( S� L�)
;
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(b)
(ii) P( L� ) .
Find the probability that
[4]
(i)
Katie goes to the shopping mall and she is not late;
(ii) Sandy goes to the shopping mall, given that the person who goes to the
shopping mall arrives home late.
[5]
The attendance of Sandy is recorded for two particular days when she goes to the
shopping mall. If one lateness is marked, she will be penalized by a $10 fee reduction. If
two latenesses are marked, she will be penalized by a $25 fee reduction. Let X be the
total amount of fee reduction for Sandy.
(c)
Copy and complete the probability distribution table.
X 0 10 25
P( X � x)
[3]
(d) Calculate the expected value of X .
[2]
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