Question

A diner asks patrons for their preference for waffles or pancakes and syrup or fruit topping.

Answer 1

Answer:

$P (Waffles | Syrup)\neq P(Waffles)$

Step-by-step explanation:

From the table we have to:

Probability of syrup is 0.96

Probability of waffles and syrup is 0.32

P (Waffles | Syrup) = P (Waffles and syrup) / P (syrup)

So:

If this equality is met, the probabilities are dependent, if on the contrary

P (Wafles | Syrup) = P (Wafles) then are independent probabilities.

$P (Wafles | Syrup) = 0.32 / 0.96 = 0.333 \neq 0.32$

So we have to:

$P (Waffles | Syrup)\neq P(Waffles)$

The probabilities are dependent.

Answer 2

Answer:

Preference for waffies and syrup are dependent events and

$P(waffies\mid syrup)\neq P(waffies)$

Step-by-step explanation:

Since we have given that

$P(waffies)=0.34$

$P(syrup\cap waffies)=0.32$

As we know that if A and B are independent it must satisfy ,

$PA\cap B)=P(A).P(B)$

But here,

$P(waffies\cap syrup)\neq P(waffies).P(syrup)\\0.32\neq 0.34\times 0.96\\0.32\neq 0.3264$

Hence, they are not independent i.e. they are dependent.

And

$P(waffies\mid syrup)\neq P(waffies)$

Because,

$P(waffies\mid syrup)\\\\=\frac{P(waffies\cap syrup)}{P(syrup)}\\\\=\frac{0.32}{0.96}\\\\=0.33$

but,

$P(waffies)=0.34$