Question

There is a 70% chance that a person eats dinner, a 50% chance a person eats dessert and a 35% chance the person will eat dinner and dessert. Which of the following is true?
A. Eating dinner and eating dessert are dependent events because P(dinner)*P(dessert)=0.7*0.5=0.35 which is equal to P(dinner and dessert)=0.35.
B. Eating dinner and eating dessert are independent events becauseP(dinner)-P(dessert)=0.7-0.5=0.2 which is less than P(dinner and dessert)=0.35.
C. Eating dinner and eating dessert are dependent events because P(dinner)-P(dessert)=0.7-0.5=0.2 which is less than P(dinnerand dessert)=0.35.
D. Eating dinner and eating dessert are independent events because P(dinner)*P(dessert)=0.7*0.5=0.35 which is equal to P(dinnerand dessert)=0.35.

Answer 1

From probability we know that if we have two independent events, A and B, then we know that to find the probability that two independent events will happen we multiply the probabilities of the two events.

Thus, to find the probability, P(A and B), we simply have to use the following equation:

P(A and B)=$P(A)\times P(B)$

Now, in our question, the situation is similar. We have been given that "There is a 70% chance that a person eats dinner, a 50% chance a person eats dessert and a 35% chance the person will eat dinner and dessert."

Let "A" be the event that a person eats dinner.

Let "B" be the event that a person eats dessert.

We can see that events A and B are independent events because a person who has dinner may not necessarily have desserts and vice versa.

Now, it has been given that $P(A)=0.7$ and $P(B)=0.5$. Therefore the probability that a person who has dinner will have dessert too will be given by:

P(A and B)=$P(A)\times P(B)=0.7\times 0.5=0.35$

Thus, out of the given options, only Option D is the correct option.

Answer 2

I think the answer is A.