# 13.&nbsp;&nbsp; A psychologist determined that the...

13.   A psychologist determined that thenumber of sessions required to obtain the trust of a new patient iseither 1,2, or 3. Let x be a random variable indicating thenumber of session required to gain the patients trust. Thefollowing probability function has been proposed.
f(x) =x/6              for x = 1, 2, or 3

a. is this probability function valid? Explain
b. what is the probability that takes exactly 2 sessionsto gain the patients trust
c. what is the probability that it takes at least 2 sessionsto gain the patients trust
51. Of the 25 students (14 boys and 11 girls) in the 6thgrade class at St. Andrews school, 5 students were absentthursday.
a. what is the probability that 2 of the absent studentswere girls?
b.  what is the probability that 2 of theabsent students were boys?
c. what is the probability that all the absentstudents were boys?
d. what is the probability   that none of theabsent students were boys?

1. We know that p(x)=1 p(x = (1/6)+(2/6)+(3/6) =1
Therefore it is a valid probabilityfunction.
prob.that takes exactly 2 sessions to gain thepatients trust is   p(x=2) =2/6
prob.that it takes atleast 2 sessions to gain thepatients trust is p(x 2)=(2/6)+(3/6)

51. 5 absent students can be selected from 25 in ways
2 absent girlstudents can be selected from 11 girls in ways
3 absent boysstudents can be selected from 14 boys in ways
probability that 2 of absentgirls is *   Similarly
probability that 2 of the absentees were boysis   probability that all the absentees were boys is   probability that none of the absent astudents were boys is   