Question

1. Assume that random guess are made for five multiple-choice questions on an ACT test, so that n = 5, and p = 0.20. Find the indicated probability for the number of correct answers.

a. Find the probability that the number of correct answers is exactly 4.

b. Find the probability that the number of correct answers is at least 3.

Answer 1

Solution :

Given that ,

p = 0.20

1 - p = 1 -0.20 = 0.80

n = 5

Using binomial probability formula ,

P(X = x) = ((n! / (n - x)!) * p^x * (1 - p)^{n - x}

a ) P(X = 4) = ((5! / (5 - 4)!) * 0.20⁴ * 0.80^{5 - 4}

= 0.0064

Probability = 0.0064

b ) p (  x   3 )  =p (x = 3 )+ p (x = 4) + p (x = 5)

  = (5 / (5 - 3)!) * 0.20³ * 0.80)^{5 - 3}

   = (5 / (5 - 4)!) * 0.20⁴ * 0.80)^{5 - 4}

  = (5 / (5 - 5)!) * 0.20⁵* 0.80)^{5 - 5}

=0.0512 + 0.0064 + 0.00032

p (  x 3 )  =0.0579

Probability = 0.0579