Analysis and Approaches for IBDP Maths Ebook 1 | Page 273

88
Paper 2 Section A – Finding
and
probabilities with given parameters
Front Page
Example
A box holds 100 eggs. The probability that an egg is white is 0.04.
(a)
(b)
(c)
Find the expected number of white eggs in the box.
Find the probability that there are exactly 13 white eggs in the box.
Find the probability that there are at least 8 white eggs in the box.
[2]
[2]
[3]
Solution
(a) E( X )
� (100)(0.04)
(A1) for substitution
� 4
A1 N2
(b) X ~ B(100, 0.04)
P( X � 13)
�100 � (0.04)
13 (1 0.04)
100�13
��
� �
� 13 �
(M1) for valid approach
� 0.000137
A1 N2
(c) P( X � 8)
�1� P( X � 7)
(M1) for valid approach
�1� 0.952487949
(A1) for correct value
� 0.0475
A1 N3
[2]
[2]
[3]
20
Exercise 88
1. A box holds 80 apples. The probability that an apple is rotten is 0.06.
(a)
(b)
(c)
Find the expected number of rotten apples in the box.
Find the probability that there are exactly 10 rotten apples in the box.
Find the probability that there are at least 15 rotten apples in the box.
[2]
[2]
[3]
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