Final answer:
To find the probability that a student has a brother given that they do not have a sister, we need to use conditional probability. The probability is 13/19, or approximately 0.684.
Step-by-step explanation:
To find the probability that a student has a brother given that they do not have a sister, we need to use conditional probability.
First, we need to find the number of students who have a brother but do not have a sister. Out of the 22 students, there are 13 who have a brother and 15 who have a sister.
Since there are 3 students who do not have any siblings, there are 22 - 3 = 19 students who have at least one sibling.
Out of these 19 students, 13 have a brother.
Therefore, the probability that a student has a brother given that they do not have a sister is 13/19, or approximately 0.684.