Question

1. Pat Statsdud is a (not good) student taking a statistics course. Pat’s strategy is to rely on luck for the next quiz. The quiz consists of 10 multiple-choice questions. Each question has four possible answers, only one of which is correct. Pat plans to guess the answer to each question.If 60% or above is pass. what is P (passing) ?

   		roughly 2%
   		roughly 1%
   		roughly 0.1%
   		roughly 0.001%

Answer 1

Solution :

Given :

n = 10

Each question has 4 possible answers. So ,probability of getting answer correct = p = 1/4 = 0.25

X be the number of correct answers

X follows Binomial(n = 10 , p = 0.25)

Using binomial probability formula :

P(X = x) = (_nC_x) * p^x * (1 - p)^n-x ; x = 0 ,1 , 2 , ....., n

Passing criteria : 60% and above

60% of 10 = 6

So , P(passing) = P(60% and above)

= P(X 6)

= 1 - {P(X < 6) }

= 1 - {P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) }

= 1 - { (₁₀C₀) * 0.25⁰ * (0.75)^10-0 + (₁₀C₁) * 0.25¹ * (0.75)^10-1 + (₁₀C₂) * 0.25² * (0.75)^10-2 + (₁₀C₃) * 0.25³ * (0.75)^10-3 + (₁₀C₄) * 0.25⁴ * (0.75)^10-4 + (₁₀C₅) * 0.25⁵ * (0.75)^10-5}

= 1 - { 0.05631351471 + 0.1877117157 + 0.28156757355+ 0.2502822876 + 0.1459980011 + 0.05839920044}

= 1 - {0.98027229309}

= 0.01972770691

= 1.97%

= roughly 2%

Thus, Alternative second is correct Option.