Answer to Question #123892 in Statistics and Probability for Eric Yamoah

Question

The marketing director of Ghana DASCO Electronics was interested in studying the intention of consumers to purchase new large TV set in 2020 and as a follow- up, whether they in fact actually purchased the television. Suppose that a sample of 1000 household was initially selected and the respondents were asked whether they planned to purchase a large DASCO TV. Twelve months later the same respondents were asked whether they actually purchased the television. The results are summarized in the table below

Planned to Purchase Yes No Total

Yes 200 50 250

No 100 650 750

Total 300 700

Find the probability of selecting a respondent who actually purchased a large television. Interpret your answer in a simple single sentence.

Compute the marginal probability of planning to purchase a large television.

Answer 1

$H_1$ --- "choose a respondent who planned to purchase".

$H_2$ --- "choose a respondent who did not plan to purchase".

Events $H_1$ and $H_2$ create a full group of hypothesis.

$A$ --- "choose a respondent who actually purchased".

We use the formula of full probability:

$P(A)=P(H_1)P(A|H_1)+P(H_2)P(A|H_2)\\ P(A)=\frac{300}{1000}\frac{200}{300}+\frac{700}{1000}\frac{50}{700}=\\ =0.25\\ \text{Probability of selecting a respondent who actually}\\ \text{purchased a large television is equal to }0.25.$

b) --- marginal probability of planning to purchase

"P("Yes")=\\frac{200+100}{1000}=0.3\\\\\nP("No")=\\frac{50+650}{1000}=0.7"