Analysis and Approaches for IBDP Maths Ebook 1 | Page 268

Your Practice Set – Analysis and Approaches for IBDP Mathematics
2. In a game, two standard six-sided dice are tossed. Let X be the sum of the scores on the
two dice.
(a)
Find
(b)
(i) P( X � 8) ;
(ii) P( X � 8) ;
(iii) P( X �9 X � 8) .
Rick plays a game where he tosses two dice.
If the sum is 8, he wins 5 points.
If the sum is greater than 8, he wins k points.
If the sum is less than 8, he loses 1 point.
Find the value of k for which Rick’s expected number of points is one.
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[7]
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) .
[5]
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.
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