P(x)=(n−x)!x!n!pxqn−x
where p=1/5,q=1−p=4/5
So,
a) n=10
P(2)=(10−2)!2!10!(51)2(54)10−2=1.8∗0.168=0.302=30.2%
b) n=20
P(≥5)=1−P(<5)=1−P(=0)−P(=1)−P(=2)−P(=3)−P(=4)
=1−(20−0)!0!20!(51)0(54)20−0−(20−1)!1!20!(51)1(54)20−1−(20−2)!2!20!(51)2(54)20−2−(20−3)!3!20!(51)3(54)20−3−(20−4)!4!20!(51)4(54)20−4=
=1−0.0115−0.0576−0.137−0.205−0.218=0.3709=37.9%
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