a Let's examine each statement part by part to determine the number of clients who hadn’tvisitedEnglandorFrance, who had visited onlyEngland, who had visited onlyFrance and who had visited bothEnglandandFrance.
60 clients had visited England, France or both. In this case, we can find the number of clients who whohadn’tvisitedEnglandorFrance as follows.
70−60=10
Thus, 10 of 70 clients hadn’tvisitedEnglandorFrance.
Of those 60 clients, 45 had visited England. This means that rest of those 60 clients had visited onlyFrance.
60−45=15
15 clients had visited onlyFrance.
Of those 60 clients, 50 had visited France. In this case, we can find the number of clients who had visited onlyEngland by subtracting 50 from 60.
60−50=10
As a result, 10 of 60 clients had visited onlyEngland. Before we create our Venn diagram, we need to find the number of clients who had visited bothEnglandandFrance. To do that, we will first add the number of clients who had visited onlyFrance and onlyEngland.
15+10=25
Then, we will subtract this number from 60.
60−25=35
Thus, 35 of the clients had visited bothEnglandandFrance. Finally, we are ready to create the Venn diagram.
b Let p represents a client who has visited England and q represents a client who has visited France. If this is the case, let's write compound statements that represent each region of our Venn diagram.
OnlyEngland⇒p∧¬q
OnlyFrance⇒¬p∧q
BothEnglandandFrance⇒p∧q
NeitherEnglandorFrance⇒¬p∧¬q
c The formula to calculate the probability of an event is given below.
P=PossibleoutcomesFavorableoutcomes
Since our number of favorable outcomes is 35 and number of possible outcomes is 70, we can find the probability as follows.
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