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.
Plays guitar does not play guitar total
Left-handed 166 25 141
Right-handed 28 31 59
Total 144 56 200
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
To determine if events A and B are independent, we need to calculate the probability of A given B and compare it to the probability of A.
The probability of A can be calculated by the number of left-handed students who play guitar divided by the total number of students:
P(A) = 166 / 200 = 0.83
The probability of A given B can be calculated by the number of left-handed students who play guitar divided by the total number of left-handed students:
P(A|B) = 166 / 144 = 1.15
If events A and B are independent, then P(A|B) = P(A). Since P(A|B) is not equal to P(A), we can conclude that events A and B are not independent.
The strategy used to determine independence was to calculate the conditional probability of A given B and compare it to the marginal probability of A. If the two probabilities are equal, then events A and B are independent. If the two probabilities are not equal, then events A and B are not independent.