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Assume that random guesses are made for six multiple-choice questions on a test with five choices for each question so that there are n equals six trials each with the probability of success (correct) given by P equals 0.20. Find the probability of no correct answers.

Sagot :

Given in the question:

a.) Random guesses are made for six multiple-choice questions.

b.) There are five choices for each question.

c.) There are n equals six trials each with the probability of success (correct) given by P equals 0.20.

We will be using the Binomial Probability Formula:

[tex]P(X=k)=(_nC_k)(p^k)(1-p)^{n-k}[/tex]

Where,

n = Number of trials = 6

P = Probability of success = 0.20

X = Correct answers

Let's evaluate the definition of binomial probability at k = 0 since we are tasked to find the probability of no correct answers.

[tex]P(X=0)=(_6C_0)(0.20^0)(1-0.20)^{6-0}[/tex][tex]P(X=0)\text{ = (}\frac{6!}{0!(6-0)!})(0.20^0)(0.80^6)^{}^{}[/tex][tex]P(X=0)\text{ = }0.262144\text{ }\approx\text{ 0.26}2[/tex]

Therefore, the probability of no correct answers is 0.262 or 26.20%.

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