Analysis and Approaches for IBDP Maths Ebook 1 | Page 267

Front Page
(iii) P( X �11 X � 9)
P( X �11� X � 9)
�
P( X � 9)
M1
P( X �11)
�
P( X � 9)
2
� 36
1 1
�
12 12
1
�
3
A1 N2
(b) P( X � 10)
�1� P( X �10) � P( X � 10)
M1
1 1 5
�1� � � 12 12 6
A1
E( X ) � 0
M1
(2)P( X �10) � (1)P( X �10) � ( �k)P( X �10) � 0 M1
� 1 � � 1 � � 5 �
�(2) � � � (1) � � � ( �k) � � � 0
�12 � �12 � � 6 �
A2
2�1�10k
� 0
3
k �
10
A1 N4
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Exercise 86
1. 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 � 5) ;
(ii) P( X � 5) ;
(iii) P( X �4 X � 6) .
Macy plays a game where she tosses two dice.
If the sum is 5, she wins 3 points.
If the sum is less than 5, she wins 2 points.
If the sum is greater than 5, she loses k points.
Find the value of k for which Macy’s expected number of points is zero.
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[7]
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