Analysis and Approaches for IBDP Maths Ebook 1 | Seite 277

Front Page
90
Paper 2 Section B – Finding the number
of trials from a distribution
Example
Ruby goes to school five days a week. When it rains, the probability that she goes to
school by taxi is 0.7. When it does not rain, the probability that she goes to school by taxi
is 0.1. The probability that it rains on any given day is 0.32.
(a)
(b)
(c)
(d)
On a randomly selected school day, find the probability that Ruby goes to school
by taxi.
Given that Ruby went to school by taxi on Friday, find the probability that it was
raining.
In a randomly chosen school week, find the probability that Ruby goes to school
by taxi on exactly two days.
[2]
After n school days, the probability that Ruby goes to school by taxi at least once
is greater than 0.9. Find the least value of n .
[5]
[4]
[3]
Solution
20
(a) The required probability
� (0.32)(0.7) � (1 � 0.32)(0.1)
(M1)(A1) for valid approach
�(0.32)(0.7) � (0.68)(0.1)
(A1) for simplification
� 0.292
A1 N3
[4]
(b) The required probability
(0.32)(0.7)
�
0.292
(R1)A1 for correct formula
� 0.767
A1 N2
[3]
(c) X ~ B(5, 0.292)
(R1) for binomial distribution
P( X � 2)
�5 � (0.292)
2 (1 0.292)
5�2
�� � �
�2�
� 0.303
A1 N2
[2]
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