Question

Suppose that you are taking a T/F exam and you have no idea at all about the answers to the last three questions. You choose answers randomly and therefore have a 50/50 chance of being correct on any one question. 1) what is the probability that you guessed right on exactly one of the three questions? [a] 2) what is the probability that you guessed right on zero of the three questions? [b] 3) what is the probability that you guessed right on at least two of the questions? [c]

Answer 1

0.375, 0.125, 0.5

Explanation:

given that you are taking a T/F exam and you have no idea at all about the answers to the last three questions.

Probability for correct guess = 0.5 remains constant for each of the three questions

X - no of questions is binomial with n =3 and p = 0.5

1) the probability that you guessed right on exactly one of the three questions

= P(X=1)

=
`3C1(0.5)^3 = 0.375`

2) the probability that you guessed right on zero of the three questions

=
`P(X=0)\\= 0.5^3=0.125`

3) the probability that you guessed right on at least two of the questions

=
`P(x=3)+P(2)\\= 1-0.5\\=0.5`