Apps. and Interpretation for IBDP Maths Ebook 1 | Page 299

85
Paper 2 – Unknown Number of Trials
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)
Solution
On a randomly selected school day, find the probability that Ruby goes to school
by taxi.
[3]
Given that Ruby went to school by taxi on Friday, find the probability that it was
raining.
[3]
In a randomly chosen school week, find the probability that Ruby goes to school
by taxi on exactly two days.
[3]
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]
20
(a)
The required probability
� (0.32)(0.7) � (1 � 0.32)(0.1)
(M1)(A1) for substitution
� 0.292
A1 N3
[3]
(b) The required probability
(0.32)(0.7)
�
0.292
(M1)(A1) for substitution
� 0.767
A1 N3
[3]
(c) X ~ B(5, 0.292)
(R1) for binomial distribution
P( X � 2)
�5 � (0.292)
2 (1 0.292)
5�2
�� � �
(A1) for substitution
�2�
� 0.303
A1 N3
[3]
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