Pass a test

The student has to pass a test that contains 10 questions. For each of them, he chooses one of 5 answers, with just one being correct. The student did not prepare for the test, so he chooses the answers at random. What are the probabilities that the student will answer correctly:
a) a maximum of 3 questions
b) at least 4 questions
c) all 10 questions

Correct answer:

a =  0.8791
b =  0.1209
c =  0

Step-by-step explanation:

n=10 p=1/5=51=0.2  p0=(0n)p0(1p)n0=(010)0.20(10.2)1000.1074 p1=(1n)p1(1p)n1=(110)0.21(10.2)1010.2684 p2=(2n)p2(1p)n2=(210)0.22(10.2)1020.302 p3=(3n)p3(1p)n3=(310)0.23(10.2)1030.2013  a=p0+p1+p2+p3=0.1074+0.2684+0.302+0.2013=0.8791
b=1a=10.8791=0.1209
c=(10n)p10(1p)n10=(1010)0.210(10.2)1010=0



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