1. ## computing probability

A 10-question multiple-choice exam is given, and each question has five possible answers. Pascal Gonyo takes this exam and guesses at every question. Use the binomial probability formula to find the probability (to 5 decimal places) that

a) he gets exactly 2 questions correct.

b) he gets no questions correct.

c) he gets at least 1 question correct (use the information from part (b) to answer this part).

d) he gets at least 9 questions correct.

e) Without using the binomial probability that he gets exactly 2 questions correct.

f) Compare your answer to parts (a) and (e). If they are not the same explain why.

2. Originally Posted by harry
A 10-question multiple-choice exam is given, and each question has five possible answers. Pascal Gonyo takes this exam and guesses at every question. Use the binomial probability formula to find the probability (to 5 decimal places) that
Probability that he gets one write is 1/5.
Probability that he gets one wrong is 4/5.

a) he gets exactly 2 questions correct.
$\displaystyle {{10}\choose 2}(1/5)^2(4/5)^8$

b) he gets no questions correct.
$\displaystyle {{10}\choose 0}(1/5)^0(4/5)^{10}$

c) he gets at least 1 question correct (use the information from part (b) to answer this part).
$\displaystyle 1-{{10}\choose 0}(1/5)^0(4/5)^{10}$

d) he gets at least 9 questions correct.
$\displaystyle {{10}\choose 9}(1/5)^9(4/5)^1+{{10}\choose {10}}(1/5)^{10}(4/5)^0$