Suppose there are eight students sitting in the last row of the classroom. The g
ID: 3172609 • Letter: S
Question
Suppose there are eight students sitting in the last row of the classroom. The gender and age of each of these students is shown in the table below. One of these students is to be selected at random and asked a penetrating question by the professor. Evaluate the following probabilities.
Gender
Age
F
20
F
21
M
21
M
25
F
28
F
20
M
19
F
22
P(the student is younger than 23) = __________
P(the student is female) = ____________
P(the student is under 23 and female) = __________
P(the student is under 23 if the student is female) = ________
P(the student is either under 23 or female) = _________
Gender
Age
F
20
F
21
M
21
M
25
F
28
F
20
M
19
F
22
Explanation / Answer
Total 8 student
Number of ways of the selection of the 1 student from 8 is 8C1
Let Probability of the studentyounger that 23 = P(<23)
Number of student with age less than 23 are 6
So selection of student out of 6 is 6C1
So P(<23)= 6C1/8C1 = 6/8 = 3/4
Let Probability of student is female is P(Female)
Number of female is 5
So selection from the number of female is = 5C1
So
P(Female) = 5C1 /8C1 = 5/8
P(student is under 23 and female) = P(<23 &female)= P(<23) x P(female)
From formulae P(A&B)=P(A)xP(B)
P(student is under 23 and female)= 3/4 x 5/8 = 15/32
P( the student is under 23 if student is female ) is a conditional probability so conditions is that student is female find the probability of the student is under 23 let it is
P(<23/Female)
From formulae P(A/B)= P(female student with age under 23)/P(student id female)
P(student is female)=5/8
4 female student which are under 23 selected 1 female from 4 , so ways = 4C1
=4C1/8C1= 4/8 = 1/2
P(female student with age under 23) = 1/2
P(<23/Female) =(1/2)/ (5/8 ) = 4/5
P( student under 23 or student is female ) = P(student under 23 )+ P (student is female) –P(under 23 female student)
P( student under 23 or student is female )= 3/4 + 5/8 – 1/2 = 7/8
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