Question

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

Answer 1

Complete Question

Assume that random guesses are made for 7 ​multiple-choice questions on a test with 5 choices for each​ question, so that there are n=7 ​trials, each with probability of success​ (correct) given by p=0.20. Find the probability of no correct answers.

Answer:

The probability is
`P(X = 0 ) = 0.210`

Explanation:

From the question we are told that

The number of trial is n = 7

The probability of success is p = 0.20

Generally the probability of failure is

`q = 1- 0.20`

`q = 0.80`

Given that this choices follow a binomial distribution as there is only two probabilities i.e success or failure

Then the probability is mathematically represented as

`P(X = 0 ) = \left n} \atop {}} \right. C_0 * p^(0) * q^(n- 0)`

`P(X = 0 ) = \left 7} \atop {}} \right. C_0 * (0.2)^(0) * (0.8)^(7- 0)`

Here
`\left 7} \atop {}} \right. C_0 = 1`

=>
`P(X = 0 ) = 1 * 1* (0.8)^(7- 0)`

=>
`P(X = 0 ) = 0.210`