Answer to Question #244670 in Statistics and Probability for sink

Question

Assume that random guesses are made for eight multiple choice questions on an SAT​ test, so that there are n=8 ​trials, each with probability of success​ (correct) given by p=0.4. Find the indicated probability for the number of correct answers.

Answer 1

n = 8

p = 0.4

Let x be the number of correct answers.

P(x = 0) = C(8, 0) 0.4⁰ (0.6)⁸ = 0.016796

P(x = 1) = C(8, 1) 0.4¹ (0.6)⁷ = 0.089580

P(x = 2) = C(8, 2) 0.4² (0.6)⁶ = 0.209019

P(x = 3) = C(8, 3) 0.4³ (0.6)⁵ = 0.278692

P(x = 4) = C(8, 4) 0.4⁴ (0.6)⁴ = 0.232243

P(x = 5) = C(8, 5) 0.4⁵ (0.6)³ = 0.123863

P(x = 6) = C(8, 6) 0.4⁶ (0.6)² = 0.041288

P(x = 7) = C(8, 7) 0.4⁷ (0.6)¹ = 0.007864

P(x = 8) = C(8, 8) 0.4⁸ (0.6)⁰ = 0.000655