Answer to Question #123912 in Statistics and Probability for Albert Kakra Baiden

Question #123912

The marketing director of GH HOTEL was interested in studying the intention of consumers
to visit their facility after the president has fully lifted the restriction on public gathering in
2020 and as a follow- up, whether they in fact actually visited. Suppose that a sample of 1000
household was initially selected and the respondents were asked whether they planned to visit
GH HOTEL. Twelve months later the same respondents were asked whether they actually
visited the hotel. The results are summarized in the table below
Planned to visit Yes No Total
Yes 200 50 250
No 100 650 750
Total 300 700 1000
i. Draw a tree diagram to represent the information in the table.
ii. Find the probability of selecting a respondent who actually visited GH HOTEL.
Interpret your answer in a simple single sentence.
iii. Find the probability of panned visit or actual visit.
iv. Calculate the probability that a respondent actual

Expert's answer

Where p is represents is planned to visit, NP not planned to visit, v is visited and NV is not visited.

ii) Find the probability of selecting a respondent who actually visited GH HOTEL.

P(v)= p(p and v) +p(Np and v)

P(v) = (0.3*0.67) + (0.7*0.07)

P(v)=0.25

This could also be interpreted as the number of those who visited divided by the total number of respondents. Which is p(v) =250/1000 = 0.25

iii) Find the probability of panned visit or actual visit

P(p or v) = p(p) + p(Np and v)

P(p or v) = 0.3 + (0.7*0.07)

P(p or V) = 0.349 = 0.35

This could also be the total number of those who planned to go for a visit added together with the number of those who didn’t plan to go for a visit but went.

P( p or v) = (300+50)/1000= 0.35

iv)

P(v)= p(p and v) +p(Np and v)

P(v) = (0.3*0.67) + (0.7*0.07)

P(v)=0.25

This could also be interpreted as the number of those who visited divided by the total number of respondents. Which is p(v) =250/1000 = 0.25