For an extra dollar, customers can add a side of rice to their tacos. One third

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.

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