A survey of 168 people was carried out - Leaving Cert Mathematics - Question 1 - 2016
Question 1
A survey of 168 people was carried out. Participants were asked whether they owned a cat or a dog. Some of the results are recorded in the Venn diagram below.
(i) O... show full transcript
Worked Solution & Example Answer:A survey of 168 people was carried out - Leaving Cert Mathematics - Question 1 - 2016
Step 1
Complete the diagram below.
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Answer
In the Venn diagram:
Total surveyed: 168
People that do not own a cat or dog: 19
This means, people who own either a cat or a dog or both:
168−19=149
Total owning a cat: 64 + 37 + 19 = 121 (where 37 is those owning both)
Total owning a dog: 48 + 37 + 19 = 121 (where 37 is those owning both)
Completing the Venn diagram, we find cats: 64, dogs: 48, and both: 37.
Step 2
What is the probability that the person owned both a cat and a dog?
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Answer
To find the probability, we use the formula:
P(A)=Total outcomesNumber of favorable outcomes
Here, number of favorable outcomes for owning both a cat and a dog is 37, and total surveyed is 168:
P(both)=16837=4.51≈0.2202
Thus, the probability is approximately 0.22.
Step 3
What percentage of the people surveyed owned one animal only?
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To find the percentage who owned only one animal:
Total owning one animal: (64 - 37) for cats + (48 - 37) for dogs = 27 + 11 = 38
Therefore, percentage:
16838×100=22.62≈22.6%
Step 4
Complete the tree diagram below, and hence or otherwise, find the probability that Mandy chooses a VIP ticket on a Wednesday.
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The tree diagram consists of:
First branch choices: Balcony (B), Stalls (S)
Second branch choices: Monday (M), Wednesday (W), Friday (F)
Last branch choices: VIP (V), Show only (O)
Next, calculate:
Probability of selecting VIP on Wednesday (1 way):
Probability of choosing W: 31
Probability of choosing VIP: 21
Thus, total probability:
P(VIP∣W)=31×21=61
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