Apps. and Interpretation for IBDP Maths Ebook 1 | Page 288

Your Practice Set – Applications and Interpretation for IBDP Mathematics
81
Paper 2 – Game Problems
Example
In a game, two standard six-sided dice are tossed. Let X be the sum of the scores on the
two dice.
(a)
Find
(i) P( X � 10) ;
(ii) P( X � 10) ;
(b)
(iii) P( X �11 X � 9) .
Jenna plays a game where she tosses two dice.
[7]
If the sum is 10, she wins 2 points.
If the sum is greater than 10, she wins 1 point.
If the sum is less than 10, she loses k points.
(i) Write down the probability that the sum is less than 10.
(ii)
Hence, find the value of k for which Jenna’s expected number of points is
zero.
[5]
Solution
(a) (i) There are 3 ways such that X � 10 (A1) for correct value
3
P( X �10)
�
36
1
P( X �10)
�
12
A1 N2
(ii) There are 3 ways such that X � 10 (A1) for correct value
3
P( X �10)
�
36
1
P( X �10)
�
12
A1 N2
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