You're a farmer determine the probability that certain vegetables will be purchased. you know the following about the 100 customers the farmer provides fruits to:

The probabilities of buying each vegetable are given by the following equation:

amount buying a vegetable / total customers

a.
60 customers bought lettuce out of a total 100. Set up a fraction and simplify it:



The probability of a customer buying lettuce is 3/5, or 60%.

b.
20 customers bought carrots and lettuce out of a total 100. Set up a fraction and simplify it:



The probability of a customer buying carrots and lettuce is 1/5, or 20%.

c.
Given that the customer has already purchased lettuce, this means that there are 60 total customers that have the chance of buying carrots. Multiply the possible customers by the chance of purchasing carrots:



Given that a customer has purchased lettuce, there is a 42% chance of the customer buying carrots and lettuce, or a 21/50 chance.

d.
Given that the customer has purchased carrots, there are 70 possible customers that have the chance of buying cucumbers. Multiply the possible customers by the chance of buying a cucumber:



Given that the customer has purchased carrots, there is a 35% chance that the customer will purchase carrots and cucumbers, or a 7/20 chance.

The vertex of the quadratic function is (1.5, -.75)