Find the probability of passing if the minimum passing grade is 60 %.

Question

A quiz consists of 10 multiple-choice questions, each with 6 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 60 %.

P(pass)=？

Answer 1

Pr(>6 correct)

= Pr(6) + Pr(7)+ Pr(8)+Pr(9)+Pr(10)

=10C6(1/6)^6(5/6)^4 + 10C7(1/6)^7(5/6)^3

+ 10C8(1/6)^8(5/6)^2 + 10C9(1/6)^9(5/6)^1

+10C10(1/6)^10(5/6)^0

= [10(9)(8)(7)/4(3)(2)](1/6^6)(5^4)/6^4) +

[10(9)(8)/3(2)](1/6^7)(5/6^3) +

[10(9)/2](1/6^8)(5/6^2) +

10(1/6^9)(5/6) +

(1/6^10)

nCr = n!/r!(n-r)! Calulators often have nPr and nCr keys to calculate it for you

10C6 = 210

10C7= 120

10C8 = 45

10C9 =10

10C10 = 1

you can also find these values on Pascal's triangle or as coefficients in the binomial expansion

just one way to get all 10 correct Pr(10) = 10C10(1/6)^10

= 1/6^10

ten ways to get 9 correct out of 10 Pr(9) = 10C9(1/6)^9(5/6)

45 ways to get 8 correct out of 10, Pr(8) = 10C8(1/6)^8(5/6)^2

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