Questions: Suppose there are 9 members of a rock band: 3 guitarists, 1 lead singer, 2 backup singers, 1 bass player, and 2 drummers. No one both sings and plays an instrument. A person is randomly selected from the band. Find the given probability in fraction form. P (a backup singer)

Solution Steps

To find the probability of selecting a backup singer from the band, we need to determine the ratio of the number of backup singers to the total number of band members. The total number of band members is 9, and there are 2 backup singers. Therefore, the probability is the number of backup singers divided by the total number of members.

The total number of members in the rock band is given as \( 9 \).

The number of backup singers in the band is \( 2 \).

The probability \( P \) of selecting a backup singer is calculated using the formula: \[ P(\text{backup singer}) = \frac{\text{Number of backup singers}}{\text{Total number of members}} = \frac{2}{9} \]

Final Answer