For an extra dollar, customers can add a side of rice to their tacos. One third
ID: 3124878 • Letter: F
Question
For an extra dollar, customers can add a side of rice to their tacos. One third of customers order a side of rice. Twenty percent of all customers buy beef tacos and a side of rice. If a customer orders bean tacos, there is a 50% chance that the customer will order a side of rice. What is the probability that a customer does not get a side of rice with their tacos? What is the probability that a customer orders bean tacos and a side of rice? What is the probability that a customer orders chicken tacos and a side of rice? What is the probability that a customer buys either beef tacos or a side of rice? What is the probability that a randomly selected customer buys neither beef tacos nor a side of rice? Given that a customer orders beef tacos, what is the probability that the customer does not order a side of rice? Is whether or not a customer buys a side of rice independent of whether or not they buy beef tacos? Use the definition of independence to explain your answer. If a customer orders a side of rice, what is the probability that the customer ordered bean tacos? If possible please show work so I can trace solution and gain a better understanding. Thank you for all the help it is much appreciated.
Explanation / Answer
P(ordering Rice) = 1/3
P(Beef and Rice) = 0.20
P(Rice | Bean Tacos) = 0.50
What is the probability that a customer does not get a side of rice with their tacos?
= 1 - 1/3
= 2/3
What is the probability that a customer orders bean tacos and a side of rice?
P ( Rice and Bean Tacos) = P ( Rice | Bean Tacos) * P ( Bean tacos)
.
What is the probability that a customer orders chicken tacos and a side of rice?
P ( Rice and Chicken Tacos) = P ( Rice | chicken Tacos) * P ( chicken tacos)
OR P ( Rice and Chicken Tacos) = P (Rice) + P (Chicken Tacos) - P ( Rice or chicken tacos)
.
What is the probability that a customer buys either beef tacos or a side of rice?
P ( Beef or Rice) = P (Beef) + P (Rice) - P (Beef and Rice)
.
What is the probability that a randomly selected customer buys neither beef tacos nor a side of rice?
= 1 - P ( Beef or Rice)
.
Given that a customer orders beef tacos, what is the probability that the customer does not order a side of rice?
(Draw venn diagram to solve this)
.
Is whether or not a customer buys a side of rice independent of whether or not they buy beef tacos? Use the definition of independence to explain your answer.
IF P ( Rice and Beef tacos) = P (Rice) * P( Beef tacos) then the events are independent. Else not.
.
If a customer orders a side of rice, what is the probability that the customer ordered bean tacos?
P (Bean Tacos | Rice) = P (Bean tacos and Rice) / P (Rice)
(There are some missing values for the probabilities which are not given in your question. ?Put those values in the above formulae and you'll get the answer.