Solve the problem.
-A test has 11 questions. Seven questions are true/false and four are multiple-choice. Each multiple-choice question has 3 possible responses of which exactly one is correct. Find the
Probability that a student guesses on each question and gets a perfect score.
A) $\frac { 209 } { 10368 } \approx 0.020158$
B) $\frac { 1 } { 10,368 } \approx 0.000096$
C) $\frac { 1 } { 3,136 } \approx 0.000319$
D) $\frac { 1 } { 168 } \approx 0.005952$

Question

Solve the problem.
-A test has 11 questions. Seven questions are true/false and four are multiple-choice. Each multiple-choice question has 3 possible responses of which exactly one is correct. Find the
Probability that a student guesses on each question and gets a perfect score. 
A) $\frac { 209 } { 10368 } \approx 0.020158$
B) $\frac { 1 } { 10,368 } \approx 0.000096$
C) $\frac { 1 } { 3,136 } \approx 0.000319$
D) $\frac { 1 } { 168 } \approx 0.005952$

Quizplus · Accepted Answer

The probability of guessing all 7 true/false questions correctly is $ \left(\frac{1}{2}\right)^7 $. The probability of guessing all 4 multiple-choice questions correctly is $ \left(\frac{1}{3}\right)^4 $. The combined probability is $ \left(\frac{1}{2}\right)^7 \times \left(\frac{1}{3}\right)^4 = \frac{1}{128} \times \frac{1}{81} = \frac{1}{10,368} $.

Solve the Problem 20910368≈0.020158\frac { 209 } { 10368 } \approx 0.02015810368209​≈0.020158

Solve the Problem $\frac { 209 } { 10368 } \approx 0.020158$