MATH SOLVE

4 months ago

Q:
# You take a three-question true or false quiz. You guess on all the questions. What is the probability that you will get a perfect score?

Accepted Solution

A:

The probability that you will guess the first answer correctly = 1/2 = 0.5

The probability that you will guess the second answer correctly = 1/2 = 0.5

The probability that you will guess the third answer correctly = 1/2 = 0.5

The probability that you will guess all three answers correctly is

(0.5) x (0.5) x (0.5) = 0.125 = 12.5% .

============================

Here are all the ways your answer sheet could wind up:

(R = a right answer. W = a wrong answer.)

W W W

W W R

W R W

W R R

R W W

R W R

R R W

R R R

Number of possible ways to score 0 right out of 3 questions: 1 way

Number of possible ways to score 1 right out of 3 questions: 3 ways

Number of possible ways to score 2 right out of 3 questions: 3 ways

Number of possible ways to score 3 right out of 3 questions: 1 way

Statistically, if your answers are all pure guesses,

then on the average, the score you expect is

(0 + 33-1/3 + 33-1/3 + 33-1/3 + 66-2/3 + 66-2/3 + 66-2/3 + 100) / 8

= 400 / 8

= 50% .

If you're happy with that score, great !

Go to the movies the night before the test,

and start guessing.

The probability that you will guess the second answer correctly = 1/2 = 0.5

The probability that you will guess the third answer correctly = 1/2 = 0.5

The probability that you will guess all three answers correctly is

(0.5) x (0.5) x (0.5) = 0.125 = 12.5% .

============================

Here are all the ways your answer sheet could wind up:

(R = a right answer. W = a wrong answer.)

W W W

W W R

W R W

W R R

R W W

R W R

R R W

R R R

Number of possible ways to score 0 right out of 3 questions: 1 way

Number of possible ways to score 1 right out of 3 questions: 3 ways

Number of possible ways to score 2 right out of 3 questions: 3 ways

Number of possible ways to score 3 right out of 3 questions: 1 way

Statistically, if your answers are all pure guesses,

then on the average, the score you expect is

(0 + 33-1/3 + 33-1/3 + 33-1/3 + 66-2/3 + 66-2/3 + 66-2/3 + 100) / 8

= 400 / 8

= 50% .

If you're happy with that score, great !

Go to the movies the night before the test,

and start guessing.