In a 10-question matching test with 10 possible answers to match and no answer used more than once, what is the probability of guessing and getting every answer correct?
A)Pr(All Correct) =
B)Pr(All Correct) =
C)Pr(All Correct) =
D)Pr(All Correct) =
E)Pr(All Correct) =

Question

In a 10-question matching test with 10 possible answers to match and no answer used more than once, what is the probability of guessing and getting every answer correct? ​
A)Pr(All Correct) = 
B)Pr(All Correct) = 
C)Pr(All Correct) = 
D)Pr(All Correct) = 
E)Pr(All Correct) =

Quizplus · Accepted Answer

The probability of guessing the first question correctly is 1/10. The probability of guessing the second question correctly is 1/9 (since one answer has already been used). This continues until the probability of guessing the last question correctly is 1/1. Therefore, the probability of guessing all 10 questions correctly is (1/10) x (1/9) x (1/8) x ... x (1/1) which simplifies to 1/10!. So, the probability is approximately 0.000008%. The closest answer choice to this is D.

In a 10-Question Matching Test with 10 Possible Answers to Match