Among 110 students in a probability class On a threequestion

Among 110 students in a probability class. On a three-question exam, 29 get question 1 incorrect, 39 get question 2 incorrect, and 22 get question 3 incorrect. Further, 19 students get both questions 1 and 2 incorrect, 13 get both questions 2 and 3 incorrect, and 7 get both questions 1 and 3 incorrect. In addition, 6 get all three questions incorrect.

Find the probability that a randomly selected student:

a) Gets question 1 incorrect but gets question 2 correct.

b) Gets questions 2 and 3 incorrect but gets question 1 correct.

c) Gets all three questions correct.

Solution

a)

P= 1 /11

b)

P = 7/110

c)

P = 57/110