Question

Choose at random a person aged 20 to 39 years. Ask their age and marital status (never married, married, or widowed/divorced/separated). Offered is the probability model for 12 possible answers. Age in years 20 – 24 25 – 29 30 – 34 35 – 39 Never married 0.227 0.156 0.089 0.054 Married 0.027 0.086 0.137 0.148 Widowed/divorced/separated 0.006 0.015 0.022 0.033 (a) Is this a legitimate finite probability model? Select the correct description. No. This is not a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 . Yes. This is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 . Yes. This is a legitimate finite probability model because the probabilities are all greater than 0 and do not sum to 1 . No. This is not a legitimate finite probability model because the probabilities are all greater than 0 and do not sum to 1 . (b) What is the probability that the person chosen is a 20 ‑ to 24 ‑ year‑old who is married? (Enter your answer rounded to three decimal places.) P(20‑ to 24‑year‑old who is married)= (c) What is the probability that the person chosen is 20 – 24 years old? (Enter your answer rounded to three decimal places.) P(20–24 year old)= (d) What is the probability that the person chosen is married? (Enter your answer rounded to three decimal places.) P(married)=

Answer 1

Answer:

(a)(B)Yes. This is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 .

(b)P(20‑ to 24‑year‑old who is married)=0.027

(c)P(20–24 year old)=0.26

(d)P(married)=0.398

Step-by-step explanation:

Given the probability model below:

$\left\begin{array}{|c|c|c|c|c|} Age in years& 20 - 24& 25 - 29& 30 - 34& 35 - 39\\ Never married& 0.227& 0.156& 0.089& 0.054\\ Married &0.027& 0.086& 0.137& 0.148\\ Widowed/divorced/separated &0.006 &0.015& 0.022& 0.033\end{array}\right$

(a)

• Adding the probability for each row, we obtain: 0.227+0.156+0.089+0.054=0.526
• 0.027+0.086+0.137+0.148=0.398
• 0.006+0.015+0.022+0.033=0.076

0.526+0.398+0.076=1

Therefore this is a legitimate finite probability model because each probability is between 0 and 1 , and all sum to 1 .

(b) The probability that the person chosen is a 20‑24-year‑old who is married

P(20‑ to 24‑year‑old who is married)=0.027

(c)Probability that the person chosen is 20 – 24 years old

P(20–24 year old)=0.227+0.027+0.006=0.26

(d)Probability that the person chosen is married

• P(married)=0.027+0.086+0.137+0.148=0.398