Question

Problem 7 Your instructor in a college history course gives you a list of 20 possible essay questions from which he will randomly pick four for the final examination. Pressed for time, you prepare for only four of the questions. What is the probability these four will be on the examination? Select one: a. 0.00021 O b. 0.11321 OC. 0.0060 O d. 0.20 Oe. 0.40

Answer 1

Total ways of selecting 4 questions out of the 20 question is as

20 201 4. + (20-4]!) 20*19* 18 +17+16! 4*3*2+1+16! =5+19+3+17 = 4845 4

Total possible ways of selecting 4 question out of the four prepared questions is as

$\binom{4}{4}=\frac{4!}{4!*(4-4)!)}=1$

Therefore the required probability = possible ways/total ways = 1/4845 = 0.000206 = 0.00021

Answer: a. 0.00021

Note: We can directly obtain the above probability as (4/20)*(3/19)*(2/18)*(1/17) = 0.00021