Jamal has the following choices for his pizza: white sauce or red sauce; white cheese or yellow cheese; and mushrooms, pepperoni or sausage. What is the probability that he creates a pizza that has red sauce and mushrooms?
the probability of jamal making a pizza with red sauce and mushrooms is 2/7
The probability that he creates a pizza that has red sauce and mushrooms are:
\(\dfrac{1}{6}\)
Jamal has the following choices for his pizza:
White sauce or red sauce; white cheese or yellow cheese; and mushrooms, pepperoni or sausage.
Let A denote the event of choosing a red sauce.
and B denote the event of choosing a mushroom.
Let P denote the probability of an event.
Now we know that event A and event B are independent.
We are asked to find:
P(A∩B)
Since the two events are independent.
Hence,
\(P(A\bigcap B)=P(A)\times P(B)\)
\(P(A)=\dfrac{1}{2}\)
( Since out of 2 choices i.e. white sauce or red sauce , we have to choose red sauce)
and
\(P(B)=\dfrac{1}{3}\)
( Since, out of 3 choices i.e. mushrooms, pepperoni or sausage we have to choose mushroom)
Hence, the answer is:
\(P(A\bigcap B)=\dfrac{1}{2}\times \dfrac{1}{3}\)
i.e.
\(P(A\bigcap B)=\dfrac{1}{6}\)