I am studying for an exam on Wednesday that covers probability. But I wanted to check in here for a refresher since it's been 2 or 3 weeks since I've worked on questions like this.
85% of the pizzas offered in Mario's Pizza Palace have both meat AND cheese included in their topping. Futhermore, 95% of his pizzas have meat, GIVEN that they include cheese in their topping. If one of Mario's pizzas is selected randomly, what is the probability that it includes cheese in its topping?
P(AintersectB) = 85% meat and cheese
P( A l B) = Meat given cheese
I'm trying to make sure I set up things right before I move on.
I must find P(B) right? I designated B for cheese and A for meat.
Yes I believe so
To calculate the probability that a randomly selected pizza from Mario's Pizza Palace includes cheese in its topping, we can use Bayes' Theorem.
Let's define the events:
A: Pizza includes cheese in its topping
B: Pizza includes meat in its topping
Given the information provided, we know:
P(A ∩ B) = 85% (probability that the pizza has both meat and cheese topping)
P(B) = 95% (probability that the pizza has meat, given it has cheese topping)
We want to find P(A), the probability that the pizza has cheese topping.
Using Bayes' Theorem:
P(A) = P(A ∩ B) / P(B)
Substituting in the values we have:
P(A) = 0.85 / 0.95
Dividing 0.85 by 0.95, we get approximately 0.8947.
Therefore, the probability that a randomly selected pizza from Mario's Pizza Palace includes cheese in its topping is approximately 0.8947 or 89.47%.