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 $P(X = 0 ) = 0.210$

Step-by-step 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   $\left 7} \atop {}} \right. C_0 = 1$

=>      $P(X = 0 ) = 1 * 1* (0.8)^{7- 0}$

=>     $P(X = 0 ) = 0.210$