Question

N a random room, somewhere in Denver, 8 guitarists, 4 drummers, and 3 bass guitar players await an audition with Mindy Ramirez. She is going to pick two people at random to try out for her band. Find the probabilities:

a. P(2 drummers)
b. P(2 guitar players)
c. P(2 bass guitar players)
d. P(1 drummer and 1 guitar player)

Answer 1

To find the probabilities, we calculate the successful outcomes divided by the total possible outcomes. Each probability is determined by the combination formula.

Step-by-step explanation:

To find the probabilities in this scenario, we need to calculate the number of ways each event can occur and divide it by the total number of possible outcomes.

a. P(2 drummers): Since there are 4 drummers in the room, the probability of selecting 2 drummers is the number of ways to choose 2 out of 4 drummers divided by the total number of ways to choose any 2 people from the 15 musicians. This can be calculated using the combination formula as follows:

P(2 drummers) = C(4,2) / C(15,2)

b. P(2 guitar players): Similarly, the probability of selecting 2 guitar players is the number of ways to choose 2 out of 8 guitarists divided by the total number of ways to choose any 2 people:

P(2 guitar players) = C(8,2) / C(15,2)

c. P(2 bass guitar players): The probability of selecting 2 bass guitar players is the number of ways to choose 2 out of 3 bass guitar players divided by the total number of ways to choose any 2 people:

P(2 bass guitar players) = C(3,2) / C(15,2)

d. P(1 drummer and 1 guitar player): To calculate this probability, we need to consider the number of ways to choose 1 drummer out of 4 drummers and 1 guitar player out of 8 guitarists, divided by the total number of ways to choose any 2 people:

P(1 drummer and 1 guitar player) = (C(4,1) * C(8,1)) / C(15,2)