Answer to Question #110192 in Statistics and Probability for Yusuf

Question

Boy Girl Total
Speech Therapist 90 30
Neuropsychologist 45 15
Psychiatrist 30
Total 55

Question 27
What is the probability that a randomly chosen child is a boy given that he consulted with a Neuropsychologist?
(1) 0.975
(2) 0.818
(3) 0.750
(4) 0.273
(5) 0.205

Question 28
Which one of the following statements is incorrect?
(1) P(Boy) = 0.75
(2) P(Boy or Girl) = 1
(3) P(Girl or ST) = 0.795
(4) P(ST) = 0.545
(5) P(ST or NP) = 0.818

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c} & Boys & Girls & Total \\ \hline Speech \ Therapist \ (ST)& 90 & 30 & 120 \\ \hdashline Neuropsychologist\ (NP) & 45 & 15 & 60 \\ \hdashline Psychiatrist\ (P) & 30 & 10 & 40 \\ \hdashline Total & 165 & 55 & 220 \end{array}$$

Question 27

What is the probability that a randomly chosen child is a boy given that he consulted with a Neuropsychologist?  

$$P(B|NP)={45 \over60}=0.75$$

(3) 0.750 

Question 28

Which one of the following statements is incorrect?  

(1)

$$P(Boy)={165 \over220}=0.75, True$$

(2)

$$P(Boy\ or\ Girl)=1, True$$

(3)

$$P(Girl\ or\ ST)={55 \over220}+{120\over220}-{30 \over220}={29\over44}=$$

$$=0.659\not=0.795, False$$

(4)

$$P(ST)={120\over220}={6\over11}=0.545, True$$

(5)

$$P(ST\ or\ NP)={120 \over220}+{60\over220}={9 \over11}=0.818, True$$

Incorrect

(3) P(Girl or ST) = 0.795