Question

The probability of getting an A in chemistry is 46.50%. Assume randomly select 20 students enrolled in chemistry

a) what is the probability that at least 19 students receive an A in the course ?

b) what is the probability that exactly 8 students do not receive an A in the course ?

c) what is the probability that at most 18 students receive an A in the course

Answer 1

here this is binomial with parameter n=20 and p=0.465

a)

  probability that at least 19 students receive an A in the course :

P(X>=19)=P(X=19)+P(X=20)

=(20C19)*(0.465)¹⁹*(1-0.465)¹+(20C20)*(0.465)²⁰*(1-0.465)⁰ =0.0000054

b)

probability that exactly 8 students do not receive an A in the course =P(12 receive an A)

=(20C12)*(0.465)¹²(1-0.465)⁸ =0.086404

c)

probability that at most 18 students receive an A in the course =P(X<=18)=1-P(X>=19)

=1-0.0000054

=0.9999946