Question

A book publishing company surveyed 450 customers about their favorite genre and preferred season. The results are displayed in the table.


Winter Spring Summer Fall
Mystery 75 25 32 48
Romance 14 61 24 36
Sci-Fi 23 2 8 12
Non-fiction 28 22 16 24

Is preferring winter independent of favoring non-fiction books? Justify mathematically.
No, because 0.028 ≠ (0.311)(0.200)
No, because 0.062 = (0.311)(0.200)
Yes, because 0.028 ≠ (0.311)(0.200)
Yes, because 0.062 = (0.311)(0.200)

Answer 1

@toga

Answer 2

To determine if preferring winter is independent of favoring non-fiction books, we need to find the probability of preferring winter and the probability of preferring non-fiction books, and then multiply these probabilities together.

The probability of preferring winter is (75 + 14 + 23 + 28) / 450 = 0.311.

The probability of preferring non-fiction books is (28 + 22 + 16 + 24) / 450 = 0.200.

If these events were independent, then we would expect the probability of both events occurring together to be the product of their individual probabilities, or (0.311)(0.200) = 0.062.

However, the probability of preferring winter and non-fiction books is (28/450) = 0.028, which is not equal to (0.311)(0.200). Therefore, preferring winter is not independent of favoring non-fiction books.

So the correct answer is option a) No, because 0.028 ≠ (0.311)(0.200).