Question

Andrea did a survey in her statistics class and found that 18 students out of 25 use the library at least twice a week. Answer the following

(a) What is the probability that a student chosen at random from the class uses the library at least twice a week?

(b) What is the probability that a student chosen at random from the class uses the library less often than twice a week?

(c) If two students are chosen at random from the class, what is the probability that both of them use the library at least twice a week?

(d) If two students are chosen at random from the class, what is the probability that both of them do NOT use the library at least twice a week?

Answer 1

Given , total number of students=25

Number of students uses library atleast twice a week=18

a) Probability that a randomly choosen students uses library atleast twice a week=18/25= 0.72

b) Probability that a randomly choosen students uses library less often than twice a week=1- Probability that a randomly choosen students uses library atleast twice a week=1-0.72=0.28

c) one can select two students out of 25 in 25c2 ways

And, 2 students out of those who uses library atleast twice a week out of 18 such students in 18c2 ways

So, Required probability=18c2/25c2= 152/300=0.51

d) one can select 2 students who don't uses library atleast twice a week in 7c2 ways ( as 25-18=7 students don't uses library atleast twice a week)

So, probability that 2 randomly choosen students don't uses library atleast twice a week=7c2/25c2=21/300=0.07