Answer to Question #107980 in Statistics and Probability for Yusuf

Question

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

Question 25
What is the probability that a randomly chosen child who consulted with a Neuropsychologist is a boy
(1) 0.975.
(2) 0.818.
(3) 0.750.
(4) 0.273.
(5) 0.205.

Question 26
What is the probability that a randomly chosen child either consulted with a Neuropsychologist or is a boy?
(1) 0.975
(2) 0.818.
(3) 0.750.
(4) 0.273.
(5) 0.205.

Answer 1

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

What is the probability that a randomly chosen child who consulted with a Neuropsychologist is a boy

 

$${45\over 60}=0.75$$

(3) 0.750.

What is the probability that a randomly chosen child either consulted with a Neuropsychologist or is a boy? 

$$P(B\cup NP)=P(B)+B(NP)-P(B\cap NP)=$$

$$={165\over 220}+{60\over 220}-{45\over 220}={180\over 220}={9\over 11}\approx0.818$$

(2) 0.818.