Question

In a game show, a participant is asked ten multiple-choice questions. Each question has five possible answers with only one of these answers being correct. A participant wins a prize if they correctly answer seven or more of the questions. Assuming that the answer to each question is independent from each other, answer the following:

a) What is the probability that a participant who guesses blindly at all of the questions gets exactly seven correct answers?

b) What is the probability that a participant who guesses blindly at all of the questions wins a prize?

c) What is the probability of winning a prize if, on each question, a participant can eliminate three incorrect answers and then guesses blindly between the remaining two?

Answer 1

Let X is a random varable shows the number of correct answers out of 10. Here X has binomial distribution wth following parameters

n = 10 and p =1 / 5 = 0.20

(a)

The probability that a participant who guesses blindly at all of the questions gets exactly seven correct answers is

(b)

(c)

Since now person need to choose only from 2 choices so probabilty of getting correct answer only by random guess is

p = 1 / 2 = 0.50

The probability of winning a prize if, on each question, a participant can eliminate three incorrect answers and then guesses blindly between the remaining two is

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