Probability Question (Survey Based)

Question

1. A survey found that 23% of people like reading books, 44% of people like going to the movies, 12% enjoy going hiking, and 19% enjoy traveling. Find the probability that someone liked reading and traveling

-For this question because the overall percentage only reached 98% does that mean there is no overlap?

2. At a large buffet 34% of people select mashed potatoes, 32% select mac and cheese, 40% choose green beans, and 28% choose broccoli. Find the probability of someone choosing mashed potatoes and broccoli.

-I'm just not sure where to start with the overlap questions, any help is appreciated

Answer 1

Given events A and B, the probability that both A and B will occur is

P(event A) * P(event B given event A occurred).

If event A and event B are independent, then the probability that both A and B will occur is

P(event A) * P(event B)

Also: P(event A or event B) = P(event A) + P(event B) - P(event A and event B)

so P(event A and event B) = P(event A or event B) - P(event A) - P(event B)

You problem does not supply sufficient information that would lead to the determination of P(event A and event B) via either method.