Analysis and Approaches for IBDP Maths Ebook 1 | Page 269

4. In a game, there are two different boxes containing different numbered cards. The first
box contains cards numbered 2, 3 and 5. The second box contains cards numbered 2, 7
and 11. Two cards are drawn at random, one from each box. Let X be the product of the
numbers on the two cards.
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(a)
Find
(b)
(i) P( X � 33) ;
(ii) P( X � 35) ;
(iii) P( X �22 X � 33) .
Jessie plays a game where she draws two cards at random, one from each box.
If the product is 33, she wins 4k points.
If the product is greater than 33, she wins 3k points.
If the product is less than 33, she loses 2k points.
[5]
Find the value of k for which Jessie’s expected number of points is � 16 .
[7]
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