Question

# Let A represent having soup and let B represent having salad for lunch. Which statement is true? Having soup and salad for lunch are independent event

Upper level probability
Let A represent having soup and let B represent having salad for lunch.
Which statement is true?
Having soup and salad for lunch are independent events because $$\displaystyle{P}{\left({A}∣{B}\right)}={P}{\left({A}\right)}{\quad\text{and}\quad}{P}{\left({B}∣{A}\right)}={P}{\left({B}\right)}$$.
Having soup and salad for lunch are not independent because $$\displaystyle{P}{\left({A}∣{B}\right)}={P}{\left({A}\right)}{\quad\text{and}\quad}{P}{\left({B}∣{A}\right)}={P}{\left({B}\right)}$$.
Having soup and salad are not independent events because $$\displaystyle{P}{\left({A}∣{B}\right)}≠{P}{\left({A}\right)}{\quad\text{and}\quad}{P}{\left({B}∣{A}\right)}≠{P}{\left({B}\right)}$$.
Having soup and salad for lunch are independent events because $$\displaystyle{P}{\left({A}∣{B}\right)}≠{P}{\left({A}\right)}{\quad\text{and}\quad}{P}{\left({B}∣{A}\right)}≠{P}{\left({B}\right)}$$