Answer to Question #113683 in Statistics and Probability for Katenda

Question

Table below shows FK and what postings are about. Answer question 27 to 30.

C P SS Total
SM 1800 700 515 3015
TM 485 350 150 985
Total 2285 1050 665 4000

Q 27
Which statement is incorrect
1) P(SM)=0.75
2) P(SM^C)=P(TM)=0.25
3) P(C)=0.57
4) P(SS)=0.17

Q 28
Which statement is incorrect
1) P(C & SS)=0
2) P(C & SM)=0.45
3) P(C & TM)=0.12
4) P(SM | C)=0.60
5) P(SM | SS)=0.77

Q 29
Which statement is incorrect
1) SM &C are dependent
2) SM &SS are dependent
3) TM & SS are independent
4) SM &TM are mutually exclusive
5) C & P are mutually exclusive

Q 30
What is the probability that FK posting is about a SS given that the source is TM
1) 0.25
2) 0.23
3) 0.17
4) 0.15
5) 0.04

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c} & C & P & SS & Total \\ \hline CM & 1800 & 700 & 515 & 3015 \\ \hdashline TM & 485 & 350 & 150 & 985 \\ \hdashline Total & 2285 & 1050 & 665 & 4000 \end{array}$$

Q 27

Which statement is incorrect

1) P(SM)=0.75

2) P(SM^C)=P(TM)=0.25

3) P(C)=0.57

4) P(SS)=0.17 

$$P(CM)={3015\over 4000}\approx0.75$$

$$P(CM^C)=1-{3015\over 4000}\approx0.25$$

$$P(TM)={985\over 4000}\approx0.25$$

$$P(TM)={985\over 4000}=P(CM^C)$$

$$P(C)={2285\over 4000}\approx0.57$$

$$P(SS)={665\over 4000}\approx0.17$$

All statements are correct.

$$P(CM\cap C)={1800\over 4000}=0.45$$

Q 29

Which statement is incorrect

1) SM &C are dependent

2) SM &SS are dependent

3) TM & SS are independent

4) SM &TM are mutually exclusive

5) C & P are mutually exclusive 

$$P(CM)={3015\over 4000},P(C)={2285\over 4000}$$ $$P(CM)P(C)={3015\over 4000}\cdot{2285\over 4000}$$ $$P(CM\cap C)={1800\over 4000}\not={3015\over 4000}\cdot{2285\over 4000}=P(CM)P(C)$$

SM &C are dependent.

$$P(SS)={665\over 4000}$$ $$P(CM)P(SS)={3015\over 4000}\cdot{665\over 4000}$$ $$P(CM\cap SS)={515\over 4000}\not={3015\over 4000}\cdot{665\over 4000}=P(CM)P(SS)$$

SM & SS are dependent.

$$P(TM)={485\over 4000}$$

$$P(TM)P(SS)={485\over 4000}\cdot{665\over 4000}$$

$$P(TM\cap SS)={150\over 4000}\not={485\over 4000}\cdot{665\over 4000}=P(TM)P(SS)$$

TM & SS are dependent.

SM &TM are mutually exclusive.

C & P are mutually exclusive. 

Which statement is incorrect?

3) TM & SS are independent

Q 30

What is the probability that FK posting is about a SS given that the source is TM 

$$P(SS|TM)={150\over 985}={30\over197}\approx0.15$$

4) 0.15