Your math professor gives you a set of 10 problems and tells you that the final exam will consist of a random selection of 5 of them. If you figured out how to do 7 of the problems, what is the probability that you answer correctly (a) all 5 problems

0.083

Step-by-step explanation:

To solve the above question, we use the combination method.

C(n, r) = nCr = n!/r!(n - r)!

Probability of answering (all 5 correctly)

= Probability of answering ( 5 out of 7 correctly)/ Probability of answering (5 out of 10 problems)

Probability of answering ( 5 out of 7 correctly) = 7C5

nCr = n!/r!(n - r)!

= 7!/5! (7 - 5)!

= 7 × 6 × 5 × 4 × 3 × 2 × 1/( 5 × 4 × 3 × 2 × 1) × (2 × 1)

= 21 ways

Probability of answering (5 out of 10 problems) = 10C5

nCr = n!/r!(n - r)!

= 10!/5! (10 - 5)!

= 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/( 5 × 4 × 3 × 2 × 1) × (5 × 4 × 3 × 2 × 1)

= 252 ways

Probability of answering (all 5 correctly)

= 21/252

= 0.0833333333

Approximately = 0.083