chef dyer baked his famous casseroles for a company holiday party. the casseroles have different shapes and…
chef dyer baked his famous casseroles for a company holiday party. the casseroles have different shapes and different delicious fillings. what is the probability that a randomly selected casserole is shaped like a circle given that the casserole is filled with spinach? simplify any fractions.
Answer
Explanation:
Step1: Find total spinach - filled casseroles
The number of spinach - filled casseroles is the sum of rectangle - shaped and circle - shaped spinach - filled casseroles. So, $4 + 3=7$.
Step2: Find circle - shaped spinach - filled casseroles
The number of circle - shaped spinach - filled casseroles is 3.
Step3: Calculate conditional probability
The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if $A$ is the event of being circle - shaped and $B$ is the event of being spinach - filled, then the probability that a casserole is circle - shaped given it is spinach - filled is $\frac{\text{Number of circle - shaped and spinach - filled}}{\text{Number of spinach - filled}}$. So the probability is $\frac{3}{7}$.
Answer:
$\frac{3}{7}$