bruce attended a music stores banjo sale. he counted the types of banjos and made note of their discounts…
bruce attended a music stores banjo sale. he counted the types of banjos and made note of their discounts. what is the probability that a randomly selected banjo has 5 strings given that the banjo is 50% off? simplify any fractions.
Answer
Explanation:
Step1: Find number of 50% off banjos
The number of 50% off banjos is the sum of 4 - string and 5 - string banjos with 50% off. So, $4 + 4=8$.
Step2: Find number of 5 - string 50% off banjos
The number of 5 - string banjos with 50% off is 4.
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 a banjo having 5 strings and $B$ is the event of a banjo being 50% off, then $P(A|B)=\frac{\text{Number of 5 - string and 50% off}}{\text{Number of 50% off}}$. So, $P=\frac{4}{8}=\frac{1}{2}$.
Answer:
$\frac{1}{2}$