Yesterday, at a local restaurant, 60% of the customers ordered a burger.
If 42% of the customers ordered a burger and fries, what is the probability that a customer who ordered a burger also ordered fries?
If 15% of the customers ordered a burger and onion rings, what is the probability that a customer ordered onion rings given that he/she ordered a burger?
The conditional probability of event A happening given B is given by
P(A|B) = P(A∩B)/P(B)
In the example,
B=customers ordered burgers
P(B)=0.60
F=customers ordered Fries
P(B∩F)=0.42
So probability of ordering fries given the customer ordered a burger is
P(F|B)=P(B∩F)/P(B)=0.42/0.6=0.7
and similarly
R=customers ordered onion Rings
P(B∩R)=0.15
What is
P(R|B)?
To find the probability that a customer who ordered a burger also ordered fries, we need to compare the number of customers who ordered both a burger and fries to the total number of customers who ordered a burger.
We can start by finding the total percentage of customers who ordered both a burger and fries. Since 42% of the customers ordered a burger and fries, we know that 42% is the intersection of the customers who ordered a burger and those who ordered fries.
Now, we need to find the total percentage of customers who ordered a burger. We know that 60% of the customers ordered a burger, so this is our total set of customers who ordered a burger.
To find the probability, we divide the number of customers who ordered both a burger and fries (42% intersection) by the total number of customers who ordered a burger (60%). This can be represented as:
Probability = (Customers who ordered a burger and fries) / (Customers who ordered a burger)
Probability = 42% / 60%
Simplifying this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 6.
Probability = (42% ÷ 6) / (60% ÷ 6)
Probability = 7% / 10%
Therefore, the probability that a customer who ordered a burger also ordered fries is 7%.
Now, let's move on to finding the probability that a customer ordered onion rings given that he/she ordered a burger.
To find this probability, we need to compare the number of customers who ordered both a burger and onion rings to the total number of customers who ordered a burger.
We know that 15% of the customers ordered a burger and onion rings, which represents the intersection.
To find the probability, we divide the number of customers who ordered onion rings and a burger (15% intersection) by the total number of customers who ordered a burger (60%).
Probability = (Customers who ordered a burger and onion rings) / (Customers who ordered a burger)
Probability = 15% / 60%
Again, we simplify this fraction by dividing both numerator and denominator by 5.
Probability = (15% ÷ 5) / (60% ÷ 5)
Probability = 3% / 12%
Therefore, the probability that a customer ordered onion rings given that he/she ordered a burger is 3%.