SOLUTION: Suppose that an examination consists of six true and false questions, and assume that a student has no knowledge of the subject matter. The probability that the student will guess

Question 1149908: Suppose that an examination consists of six true and false questions, and assume that a student has no knowledge of the subject matter. The probability that the student will guess the correct answer to the first question is 30%. Likewise, the probability of guessing each of the remaining questions correctly is also 30%. a) What is the probability of getting more than three correct answers? b) What is the probability of getting at least two correct answers? c) What is the probability of getting at most three correct answers? d) What is the probability of getting less than five correct answers?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This is a binomial with p=0.3 and n=6
probability of 0 is 0.7^6=0.1176
of 1 is 6* 0.7^5*0.3=0.3025, the 6 from 6 different ways it can happen
of 2 is 6C2*0.7^4*.3^2=0.3241
of 3 is 6C3*0.7^3*0.3^3=0.1852
of 4 is 6C4*0.7^2*0.3^4=0.0595
of 5 is 6*0.7*0.3^5=0.0102
of 6 is .3^6=0.0007
use this for the answers
a. is 4,5,6 or 0.0704
b. at least 2 is 1- 0 and 1 or 1-0.4201 or 0.5799
c. at most 3 is probability 0,1,2,3 or the complement of a or 0.9296.
d. less than 5 is 1- 5 and 6 or 1-0.0109 or 0.9891

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