conleyjulianne
Answered

Ramone has 5 difficult questions left to answer on a multiple choice test.
Unfortunately, he is running out of time and must guess for the remaining questions.
Each question has 3 choices.
For the first 2 of these questions, he eliminated 1 of the 3 choices.
Find the probability that he will answer the first 2 questions, as well as at least 2 of the 3 remaining questions correctly.

Answer :

Blitztiger
For the first two questions, since only 2 viable choices remain, he has a [tex] \frac{1}{2} [/tex] chance on each of them. For the last 3 questions, since there are 3 choices, he has a [tex] \frac{1}{3} [/tex] chance for them.
The probability that he gets all 5 right is
[tex]( \frac{1}{2})^2 (\frac{1}{3} )^3 = \frac{1}{108}[/tex]
The probability that he gets one of the last 3 wrong, and everything else right, is:
[tex]( \frac{1}{2})^2 (\frac{1}{3} )^2 (\frac{2}{3})*3 = \frac{1}{18}[/tex]
Therefore the total probability is:
[tex]\frac{1}{108} + \frac{1}{18} = \frac{7}{108}[/tex]


Other Questions