Question

A large box of vegetables contains 6 tomatoes, 4 heads of lettuce, and 9 onions. A vegetable is chosen at random and then placed back in the box, and a second vegetable is picked. What is the probability of choosing a tomato and an onion?

Answer 1

To calculate the probability of choosing a tomato and an onion, we need to determine the individual probabilities of choosing a tomato and an onion, and then multiply them together.

P(tomato first) = (Number of tomatoes) / (Total number of vegetables)

P(tomato first) = 6 / (6 + 4 + 9) = 6 / 19

P(onion second) = (Number of onions) / (Total number of vegetables)

P(onion second) = 9 / (6 + 4 + 9) = 9 / 19

Now, to calculate the probability of choosing a tomato and an onion, we multiply these probabilities together:

P(tomato and onion) = P(tomato first) * P(onion second)

P(tomato and onion) = (6 / 19) * (9 / 19)

P(tomato and onion) = 54 / 361

Therefore, the probability of choosing a tomato and an onion is 54/361.