. Suppose that a family is leaving on a summer vacation in their camper and that

Question

. Suppose that a family is leaving on a summer vacation in their camper and that M is the event that they will experience mechanical problems, T is the event that they will receive a ticket for committing a traffic violation, and V is the event that they will arrive at a campsite with no vacancies. Referring to the following Venn diagram (each number on Venn diagram define a region, e.g., 1 is for the intersection of M and T and V), find the numbers of the regions that represent the following events: a) 2 marks] The family wll experience no mechanical problems and will not receive a ticket for a traffic violation but wll arrive at a campsite with no vacancies. b) 2 marks] The family will experience both mechanical problems and trouble in locating a campsite with a vacancy but will not receive a ticket for a traffic violation. c) 12 marks] The family will either have mechanical trouble or arrive at a campsite with no vacancies but will not receive a ticket for a traffic violation. d) [2 marks] The family will not arrive at a campsite with no vacancies

Explanation / Answer

Here we are given the following events:

Now the 4 parts to the problems - the regions they represent are shown as:

a) Here we have:

b) Now here we have:

c) Here we have:

d) Here we have:

Question Region

a) Here we have:

• no mechanical problem
• not receiving ticket for a traffic violation
• will arrive campsite with no vacancies

the only region here is 6

b) Now here we have:

• will experience mechanical problem
• not receiving ticket for a traffic violation
• will arrive campsite with no vacancies

Here we have to find intersection between events M and V but not T. Therefore the correct region here would be 2

c) Here we have:

• Have either mechanical trouble or trouble in locating campsite with no vacancy
• not receiving ticket for a traffic violation

Here the region would be either M or V but not T. This is represented by the region: 5,2 and 6

d) Here we have:

• Family will not arrive at a campsite with no vacancies.

Here we have the event not V that is represented by regions 5,4, 7 and 8

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