Apps. and Interpretation for IBDP Maths Ebook 1 | Page 293

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Paper 1 – Expected Value and Variance
Example
A biased coin is tossed for twelve times. The probability of getting a head is 0.6.
(a)
(b)
(c)
Find the expected number of heads landed.
Find the variance of the number of heads landed.
Find the probability that the number of heads landed is equal to the number of
tails landed.
[2]
[2]
[2]
Solution
(a)
(b)
(c)
The expected number
� (12)(0.6)
(A1) for substitution
� 7.2
A1 N2
The variance
�(12)(0.6)(1 � 0.6)
(A1) for substitution
� 2.88
A1 N2
The required probability
�12 � (0.6)
6 (1 0.6)
12�6
��
� �
� 6 �
(A1) for substitution
� 0.176579149
� 0.177
A1 N2
[2]
[2]
[2]
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