To determine whether carrying cash is independent of having children, we need to compare two probabilities:
1. The overall probability that an adult carries cash.
2. The conditional probability that an adult carries cash given that they have children.
Here's the breakdown:
1. Overall Probability that an Adult Carries Cash:
- According to the survey, 62% of adults carry cash on a regular basis.
- This probability can be denoted as [tex]\( P(\text{carry cash}) = 0.62 \)[/tex].
2. Conditional Probability that an Adult Carries Cash Given They Have Children:
- The survey states that 46% of adults have children, and of those, 85% carry cash on a regular basis.
- This probability can be denoted as [tex]\( P(\text{carry cash} \mid \text{have children}) = 0.85 \)[/tex].
Now, let's compare the two probabilities:
- [tex]\( P(\text{carry cash}) = 0.62 \)[/tex]
- [tex]\( P(\text{carry cash} \mid \text{have children}) = 0.85 \)[/tex]
For carrying cash to be independent of having children, these two probabilities should be equal. However, from the given values:
- [tex]\( 0.62 \neq 0.85 \)[/tex]
Since [tex]\( P(\text{carry cash}) \)[/tex] is not equal to [tex]\( P(\text{carry cash} \mid \text{have children}) \)[/tex], we can conclude that carrying cash is not independent of having children. In other words, the fact that someone has children affects the likelihood that they carry cash.
Therefore, the correct answer is:
- No, [tex]\( P(\text{carry cash}) \neq P(\text{carry cash} \mid \text{have children}) \)[/tex].
