Question

which statement is true?
using ketchup and using mustard are not independent events because ( p(a|b)
eq p(a) ) and ( p(b|a)
eq p(b) ).
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)
eq p(a) ) and ( p(b|a)
eq p(b) )
using ketchup and using mustard are independent events because ( p(a|b)=p(a) ) and ( p(b|a)=p(b) )

Explanation:

• For two events \(A\) and \(B\) to be independent, the following must hold: \(P(A|B)=P(A)\) (the probability of \(A\) occurring given that \(B\) has occurred is equal to the probability of \(A\) occurring on its own) and \(P(B|A) = P(B)\) (the probability of \(B\) occurring given that \(A\) has occurred is equal to the probability of \(B\) occurring on its own).
• If \(P(A|B)

eq P(A)\) or \(P(B|A)
eq P(B)\), the events are not independent.

Answer:

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