A group of people were asked what condiments they use on their hot dogs. They were asked whether they use ketchup, mustard, both ketchup and mustard, or neither ketchup nor mustard.

The table shows the probabilities of the results.

Use ketchup Do not use ketchup Total
Use mustard 0.2 0.48 0.68
Do not use mustard 0.15 0.17 0.32
Total 0.35 0.65
1.00

Let A represent using ketchup and B represent using mustard.

Which statement is true?

Using ketchup and using mustard are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .

Using ketchup and using mustard are independent events because P(A|B)=P(A) and P(B|A)=P(B) .

Using ketchup and using mustard are independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .

Using ketchup and using mustard are not independent events because P(A|B)=P(A) and P(B|A)=P(B) .