Question

A survey was conducted in canada to ascertain public opinion about a major national park region in the Banff -Bow valley. One question asked the amount that respondents would be willing to contribute per year to protect the environment in the Banff - Bow Valley region. the following frequency distribution was found in an article by J Ritchie et al titled "Public reaction to policy Recommendation from the Banff - Bow valley study" (journal of sustainable tourism, vol, 10 No. 4.pp 295 - 308).

For a respondent selected at random. Let

A = event that the respondent would be willing to contribute at least \(101.

B = event that the respondent would not be willing to contribute more than \)50.

C = event that the respondent would be willing to contribute between \(1 and \)200.

D = event that the respondent would be willing to contribute at least $51.

Describe the following events in words and determine the number of outcomes (respondents) that make up each event.

Part (a) (not D)

Part (b) (A & B)

Part (c) (C & A)

Part (d) (B &D)

Short answer

Part (a) Number of outcome$=85$

Part (b) Number of outcome$=0$

Part (c) Number of outcome $=219$

Part (c) Number of outcome$=116$

Step-by-step solution

Part (a) Step 1. Given information.

The following frequency distribution was discovered in the publication "Public Reactions to Policy Recommendations from the Banff-Bow Valley Study" by J. Ritchie et al.

Contribution (S)	Frequency
0	85
1 - 50	116
51 - 100	59
101 - 200	29
201 - 300	5
301 - 500	7
501 - 1000	3

For a respondent selected at random. Let

A = event that the respondent would be willing to contribute at least $101.

B = event that the respondent would not be willing to contribute more than $50.

C = event that the respondent would be willing to contribute between $1 and $200.

D = event that the respondent would be willing to contribute at least $51.

Part (a) Step 2. (not D) the event in words, as well as the number of outcomes that make it up.

(not D) is the situation in which the respondent is unwilling to provide anything.

Number of outcome$=85$

Part (b) Step 1. Given information.

The following frequency distribution was discovered in the publication "Public Reactions to Policy Recommendations from the Banff-Bow Valley Study" by J. Ritchie et al.

Contribution (S)	Frequency
0	85
1 - 50	116
51 - 100	59
101 - 200	29
201 - 300	5
301 - 500	7
501 - 1000	3

For a respondent selected at random. Let

A = event that the respondent would be willing to contribute at least $101.

B = event that the respondent would not be willing to contribute more than $50.

C = event that the respondent would be willing to contribute between $1 and $200.

D = event that the respondent would be willing to contribute at least $51.

Part (b) Step 2. The event (A & B) and the number of outcomes that make up the event.

The null event is (A & B). There are no outcomes in common between Events A and B.

Number of outcome

$(A\&B)=0$

Part (c) Step 1. Given information.

The following frequency distribution was discovered in the publication "Public Reactions to Policy Recommendations from the Banff-Bow Valley Study" by J. Ritchie et al.

Contribution (S)	Frequency
0	85
1 - 50	116
51 - 100	59
101 - 200	29
201 - 300	5
301 - 500	7
501 - 1000	3

For a respondent selected at random. Let

A = event that the respondent would be willing to contribute at least $101.

B = event that the respondent would not be willing to contribute more than $50.

C = event that the respondent would be willing to contribute between $1 and $200.

D = event that the respondent would be willing to contribute at least $51.

Part (c) Step 2. The event (C & A) and the number of outcomes that make up the event.

(C or A) is the scenario in which the respondent is willing to contribute at least $1.

Number of outcome

$$\begin{gathered} (CorA)=116+59+29+5+7+3 \\ (CorA)=219 \end{gathered}$$

Part (d) Step 1. Given information.

The following frequency distribution was discovered in the publication "Public Reactions to Policy Recommendations from the Banff-Bow Valley Study" by J. Ritchie et al.

Contribution (S)	Frequency
0	85
1 - 50	116
51 - 100	59
101 - 200	29
201 - 300	5
301 - 500	7
501 - 1000	3

For a respondent selected at random. Let

A = event that the respondent would be willing to contribute at least $101.

B = event that the respondent would not be willing to contribute more than $50.

C = event that the respondent would be willing to contribute between $1 and $200.

D = event that the respondent would be willing to contribute at least $51.

Part (d) Step 2. The event (B & D) and the number of outcomes that make up the event.

(B & D) is the scenario in which the respondent is ready to contribute somewhere between $1 and $50.

Number of outcome

$(B\&D)=116$