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. 25% off 50% off 4 strings 6 4 5 strings 6 4 what is the probability that a randomly selected banjo has 5 strings given that the banjo is 50% off? simplify any fractions.

bruce attended a music stores banjo sale. he counted the types of banjos and made note of their discounts. 25% off 50% off 4 strings 6 4 5 strings 6 4 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 total number of 50% - off banjos

Add the number of 4 - string and 5 - string banjos with 50% off. $4 + 4=8$.

Step2: Find number of 5 - string banjos with 50% off

The number of 5 - string banjos with 50% off is 4.

Step3: Calculate the conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In this case, the probability that a banjo has 5 strings given it is 50% off is $\frac{\text{Number of 5 - string 50% - off banjos}}{\text{Total number of 50% - off banjos}}=\frac{4}{8}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$