Apps. and Interpretation for IBDP Maths Ebook 1 | Page 297

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Paper 1 – Unknown Success Probability
Example
Sam likes to play a game of chance. For this game, the probability that Sam wins is p .
He plays the game ten times.
(a)
(b)
Write down an expression, in terms of p , for the probability that he wins exactly
three games.
[2]
Hence, find the possible values of p such that the probability that he wins exactly
three games is 0.22.
[3]
Solution
(a)
(b)
The required probability
�10�
3 10 3
��
� (1 )
3 p � p �
� �
(A1) for substitution
�10�
3 7
��
� (1 )
3 p � p
� �
A1 N2
�10�
3 7
� � (1 ) 0.22
3 p � p �
� �
(M1) for setting equation
�10�
3 7
� � (1 ) 0.22 0
3 p � p � �
� �
By considering the graph of
�10�
3 7
y � � �p (1 � p) � 0.22 ,
� 3 �
p � 0.216 and p � 0.394
A2 N3
[2]
[3]
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