Question

(adapted from Ross, 2.37) 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? (b) at least 4 of the proble

Answer 1

Mr. Martin’s math test, which is worth 100 points, has 35 problems. Each problem is worth either 5 points or 2 points.

Let x = the number of questions worth 5 points.

Let y = the number of questions worth 2 points.

x + y = 35,

5x + 2y = 100

How many problems of each point value are on the test?

10 problems worth 5 points and 25 problems worth 2 points

15 problems worth 5 points and 20 problems worth 2 points

20 problems worth 5 points and 15 problems worth 2 points

25 problems worth 5 points and 10 problems worth 2 points

A is the correct answer

Answer 2

(a) 1/2

(b) 9/10

Explanation:

Probability is given by number of possible outcomes ÷ number of total outcomes

(a) Number of possible outcomes = 5 questions, number of total outcomes = 10 questions

Probability (I answer all 5 problems correctly) = 5/10 = 1/2

(b) Probability (I answer at least 4 of the problems correctly) means I either answer 4 of the problems or all 5 problems correctly = 4/10 + 5/10 = 9/10