The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial.The binomial distribution is used to obtain the probability of observing x successes in n trials, with the probability of success on a single trial denoted by p. The binomial distribution assumes that p is fixed for all trials. The formula for the binomial probability mass function is
P(X=x)=(nx)px(1−p)n−x
1. Exactly 4 will have a medical aid.
P(X=4)=(104)0.34(1−0.3)10−3=0.200120949
2. At least 2 will have a medical aid.
P(X≥2)=1−P(X<2)=1−P(X=0)−P(X=1)=
=1−(100)0.30(1−0.3)10−0−(101)0.31(1−0.3)10−1=0.850692
3. More than 9 will have a medical aid.
P(X>9)=P(X=10)=(1010)0.310(1−0.3)10−10=0.000006
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