Analysis and Approaches for IBDP Maths Ebook 1 | Page 275

Front Page
89
Paper 2 Section A – Finding the success
probability from a distribution
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 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 �
� �
�10�
3 7
��
� (1 )
3 p � p
� �
A2 N2
�10�
3 7
� � (1 ) 0.22
3 p � p �
� �
(M1) for setting equation
p � 0.216 and p � 0.394
A2 N3
[2]
[3]
20
Exercise 89
1. A factory makes switches. The probability that a switch is defective is p . The factory
tests a random sample of 120 switches.
(a)
(b)
Write down an expression, in terms of p , for the probability that there are exactly
three defective switches in the sample.
[2]
Hence, find the values of p such that the probability that there are exactly three
defective switches in the sample is 0.16.
[3]
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