At a certain pizza parlor, 50% of the customers order a pizza containing onions, 49% of the customers order a pizza containing sausage, and 61% order a pizza containing onions or sausage (or both). Find the probability that a customer chosen at random will order a pizza containing both onions and sausage.Write your answer as a decimal
Question
At a certain pizza parlor, 50% of the customers order a pizza containing onions, 49% of the customers order a pizza containing sausage, and 61% order a pizza containing onions or sausage (or both). Find the probability that a customer chosen at random will order a pizza containing both onions and sausage.Write your answer as a decimal
Solution
To find the probability that a customer will order a pizza containing both onions and sausage, we can use the formula for the probability of the union of two events:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Where:
- P(A ∪ B) is the probability of event A or event B occurring (in this case, the probability of a customer ordering a pizza with onions or sausage)
- P(A) is the probability of event A occurring (the probability of a customer ordering a pizza with onions)
- P(B) is the probability of event B occurring (the probability of a customer ordering a pizza with sausage)
- P(A ∩ B) is the probability of both events A and B occurring (the probability we're trying to find)
We can rearrange the formula to solve for P(A ∩ B):
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Substituting the given probabilities:
P(A ∩ B) = 0.50 + 0.49 - 0.61 = 0.38
So, the probability that a customer chosen at random will order a pizza containing both onions and sausage is 0.38, or 38%.
Similar Questions
At a pizza shop, 70% of the customers order a pizza, 25% of the customers order a salad, and 15% of the customers order both a pizza and a salad.If a customer is chosen at random, what is the probability that he or she orders either a pizza or a salad?A.0.45B.0.95C.0.80D.0.175
At a certain fast-food restaurant, 63% of customers order a chicken sandwich, 43% of customers order french fries, and 32% of customers order both a chicken sandwich and french fries. What is the probability that a randomly selected customer will order a chicken sandwich or french fries (or both items)?2 points0.650.690.740.83
Consider a cafeteria with three meals. For a randomly selected patron, it is known that 30% of patrons get meal A,30% of patrons get meal B,40% of patrons get meal C.Suppose we randomly select two patrons. What is the probability that these people have the same meal? Calculate your answer to 4 decimal places.
In a large restaurant, an average of 2 out of every 5 customers ask for water with their meal. A random sample of 10 customers is selected.Calculate the probability taht exact 8 customers ask for water with their meal. Enter your answer as a decimal rounded to 4 decimal places
A taste test asks people from Texas and California which pasta they prefer, brand A or brand B. This table shows the results.A person is randomly selected from those tested.What is the probability that the person is from California, given that the person prefers brand A? Round your answer to two decimal places.A.0.60B.0.55C.0.53D.0.62
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.