a We want to construct a two-way table showing the number of pet owners. We will start by making an empty table with the appropriate column and row headers.
Now we will use the numbers of each type of pet owners from the Venn diagram to fill it with joint frequencies.
Finally, we will add joint frequencies in each column and row to get marginal frequencies.
People who own cat:& 36+ 25= 61
People who don't own cat:& 57+92= 149
People who own dog:& 36+ 57= 93
People who don't own dog:& 25+92=117
Let's write the newly obtained information in our table.
We have two ways of calculating the grand total. We can add the number of people who own a dog to the number of people who do not own a dog, or we can add the people who own a cat to the people who do not own a cat. These two numbers must be the same!
Grand total
l 93+117=210 61+ 149=210 ✓
Both methods returned the same result, so we did excellent work! Finally, we can complete our table.
Now we can calculate the probability that a randomly selected person does not own either pet. To do so, we have to divide the number of people who do not own either pet (92) by the number of all surveyed people (210).
92/210≈ 0.438
The probability that a randomly selected person does not own either pet is about 0.438.
b We want to find the probability that a randomly selected person who owns a dog also owns a cat. We will start by constructing a two-way table of relative frequencies to evaluate this conditional probability. To do so we will use the two-way table of frequency counts from Part A.
Finally, we will find the conditional probability of owning a cat for a person who owns a dog. Let's remember the formula for the conditional probability.
P(B|A)=P(AandB)/P(A)
Event B in the formula is owning a cat, and Event A is owning a dog. We will divide the joint relative frequency from the first column and row by the marginal frequency of the first column of this conditional probability.
