The music department instructor at school asked students if they know how to play a guitar and what their handedness was. The collected information is in the table below.

Question

Let A be the event "knows how to play guitar"
Let B be the event "is left handed"
Determine if events A and B are independent.
Explain your reasoning and the strategy you used to determine it

Answer 1

To determine if events A and B are independent, we need to calculate P(A) and P(B), and then calculate P(A and B). If P(A) * P(B) = P(A and B), then events A and B are independent.

Let's first calculate the probabilities:

P(A) = Number of students who know how to play guitar / Total number of students
P(A) = 12 / 30
P(A) = 0.4

P(B) = Number of left handed students / Total number of students
P(B) = 6 / 30
P(B) = 0.2

Next, let's calculate P(A and B):

P(A and B) = Number of students who know how to play guitar and are left handed / Total number of students
P(A and B) = 2 / 30
P(A and B) = 0.0667

Now, let's calculate P(A) * P(B):

P(A) * P(B) = 0.4 * 0.2
P(A) * P(B) = 0.08

Since P(A and B) does not equal P(A) * P(B), events A and B are not independent. This means that knowing if a student knows how to play guitar does impact the likelihood of them being left handed.