Apps. and Interpretation for IBDP Maths Ebook 1 | Page 291

3. In a game, there are two different boxes containing different numbered cards. The first
box contains cards numbered 1, 2 and 3. The second box contains cards numbered 10, 20
and 30. Two cards are drawn at random, one from each box. Let X be the sum of the
numbers on the two cards.
(a)
Find
(i) P( X � 21) ;
(ii) P( X � 21) ;
(b)
(iii) P(30 � X � 33 X � 21) .
[7]
Stephen plays a game where he draws two cards at random, one from each box.
If the sum is 21, he wins 3k points.
If the sum is greater than 21, he wins k points.
If the sum is less than 21, no points would be awarded
Find the value of k for which Stephen’s expected number of points is eight.
[6]
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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.
(a)
Find
(i) P( X � 33) ;
(ii) P( X � 35) ;
(b)
(iii) P( X �22 X � 33) .
Jessie plays a game where she draws two cards at random, one from each box.
[7]
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.
Find the value of k for which Jessie’s expected number of points is � 16 .
[6]
www.seprodstore.com
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