A survey shows that 70% of people like dogs, 50% like cats, and 20% like both. W

₹0.0

Question: A survey shows that 70% of people like dogs, 50% like cats, and 20% like both. What percentage of people like either dogs or cats?

Options:

Correct Answer: 80%

Solution:

Using inclusion-exclusion, the percentage of people who like either dogs or cats is: 70% + 50% - 20% = 100%.

A survey shows that 70% of people like dogs, 50% like cats, and 20% like both. What percentage of people like either dogs or cats?

A survey shows that 70% of people like dogs, 50% like cats, and 20% like both. What percentage of people like either dogs or cats?

Step 1: Identify the percentage of people who like dogs, which is 70%.
Step 2: Identify the percentage of people who like cats, which is 50%.
Step 3: Identify the percentage of people who like both dogs and cats, which is 20%.
Step 4: To find the percentage of people who like either dogs or cats, use the formula: (Percentage of people who like dogs) + (Percentage of people who like cats) - (Percentage of people who like both).
Step 5: Plug in the numbers: 70% + 50% - 20%.
Step 6: Calculate the result: 70 + 50 = 120, then 120 - 20 = 100.
Step 7: The final answer is that 100% of people like either dogs or cats.

Inclusion-Exclusion Principle – A method used to calculate the size of the union of two sets by adding the sizes of the individual sets and subtracting the size of their intersection.