Apps. and Interpretation for IBDP Maths Ebook 1 | Page 295

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Paper 1 – Probabilities in a Binomial Distribution
Example
A box holds 100 eggs. The probability that an egg is white is 0.04. Let X be the number
of white eggs in the box.
(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
E( X ) � 4
A1 N2
(b) P( X � 13)
�100 � (0.04)
13 (1 0.04)
100�13
��
� �
� 13 �
(A1) for substitution
� 0.000136861
� 0.000137
A1 N2
(c) P( X � 8)
�1� P( X � 7)
(M1) for valid approach
�1� 0.952487949
(A1) for correct value
� 0.047512051
� 0.0475
A1 N3
[2]
[2]
[3]
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