You take a quiz with 6 multiple-choice questions. After you studied, you estimated that you would have about an 80% chance of getting any individual question right. What are your chances of getting them all right? The random numbers below represent a simulation with 20 trials. Let 0-7 represent a correct answer and let 8-9 represent an incorrect answer.

235588 930328 391885 362974 975407 732652 591874 848259 541003 536160 342269 674938 349802 661596 672801 633052 168858 551266 463349 884658

0.262144 = 26.2% of getting all the 6 questions correctly.

Step-by-step explanation:

This is a binomial distribution problem

Binomial distribution function is represented by

P (X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 6 multiple choice questions

x = Number of successes required = 6 (we want to get it all right.

p = probability of success = 0.8 (80% chance of getting any individual question right; 0.8 probability of getting each question correctly)

q = probability of failure = 1 - 0.8 = 0.2

P (X = 6) = ⁶C₆ (0.8) ⁶ (0.2) ⁶⁻⁶ = 1 (0.262144) (1) = 0.262144