. (8 points) Your math professor gives you a set of 12 problems and says that the final exam will consist of a random selection of 6 of them. If you figured out how to do 10 of the problems, what is the probability that you answer correctly (a) all 6 of the problems

0.22727

Step-by-step explanation:

Solution:-

- The math professor gives us a set of 12 problems and out of 12 problems he will give 6 on the final exam.

- The strategy is to determine in how many ways the math professor can select those 6 problems from the set of 12 problems.

- We have to select 10 questions such that all the exam problems were the one we studied.

- The total number of ways to select the 10 questions without restriction from pool of 12 question can be determined by use of combinations:

Total ways to select 10 out of 12:    

            12 C 10 = 66 ways to select 10 questions.

 Number of ways to select 10 such that all 6 exam questions are there:

FIX                       Remaining 4:  _ _ _ _

 select 6                select other 4 : 6C4 = 15 ways

Hence, there 15 ways to select 10 such that all 6 exam problems are selected.

- The probability of all 6 problems are prepared for:

                P ( All 6 ) = Favorable outcomes / Total outcomes

                                = 15 / 66

                                 = 0.22727

73.0769230769% of the games were won

00

step-by-step explanation: