To find the probability that both of two randomly picked people own a cat, given that the probability of one person owning a cat is 69%, follow these steps:
1. Express Probability as a Decimal:
First, convert the given percentage to a decimal form. The probability that one person owns a cat is 69%, which can be written as:
[tex]\[
P(\text{one person owns a cat}) = 0.69
\][/tex]
2. Use Independence of Events:
The probability that two people both own a cat is found by multiplying the probabilities of each individual owning a cat. This is because the ownership of a cat by each person is an independent event.
3. Calculate Combined Probability:
Therefore, the probability that both randomly picked people own a cat is:
[tex]\[
P(\text{both own a cat}) = P(\text{one person owns a cat}) \times P(\text{one person owns a cat})
\][/tex]
Substituting the values:
[tex]\[
P(\text{both own a cat}) = 0.69 \times 0.69
\][/tex]
4. Perform the Multiplication:
[tex]\[
0.69 \times 0.69 = 0.4761
\][/tex]
After going through these steps, the probability that both randomly picked people own a cat is:
[tex]\[
0.476 \quad (\text{rounded to three decimal places})
\][/tex]
