To find the probability that a randomly selected person is male given that the person is left handed, we need to use the concept of conditional probability. The conditional probability [tex]\(P(A|B)\)[/tex] is given by the formula:
[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \][/tex]
Where:
- [tex]\(A\)[/tex] is the event that the person is male.
- [tex]\(B\)[/tex] is the event that the person is left handed.
First, let's identify the relevant counts from the table:
- Number of left handed males = 13
- Number of left handed females = 11
The total number of left-handed people is the sum of left handed males and left handed females:
[tex]\[ 13 + 11 = 24 \][/tex]
Now, the probability that a person is male given that the person is left handed can be found by dividing the number of left handed males by the total number of left handed people:
[tex]\[ P(\text{Male | Left Handed}) = \frac{\text{Number of Left Handed Males}}{\text{Total Number of Left Handed People}} = \frac{13}{24} \][/tex]
Therefore, the probability that a randomly selected person is male given that the person is left handed is:
[tex]\[ \frac{13}{24} \][/tex]
The correct answer from the options provided is:
4) [tex]\(\frac{13}{24}\)[/tex]
