Analysis and Approaches for IBDP Maths Ebook 1 | Page 263

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2. Sandy and Katie both wish to go to the shopping mall but one of them has to stay home to
baby-sit.
The probability that Sandy goes to the shopping mall is 0.2. Only one of them will go.
If Sandy goes to the shopping mall the probability that she is late home is 0.7.
If Katie goes to the shopping mall the probability that she is late 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.
19
(a)
Find
(b)
(i) P( S� L�)
;
(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. 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]
www.seprodstore.com
255