In order to calculate the probability that a student has a sister given that they do not have a brother, we first need to find the total number of students who do not have a brother:
Total students without a brother = students with a sister and no brother + students with no sister and no brother
Total students without a brother = 12 + 5
Total students without a brother = 17
Now, we need to find the number of students who have a sister but do not have a brother:
Students with a sister but no brother = 12
Now, we can calculate the probability that a student has a sister given that they do not have a brother:
P(student has a sister | student does not have a brother) = Students with a sister but no brother / Total students without a brother
P(student has a sister | student does not have a brother) = 12 / 17
P(student has a sister | student does not have a brother) ≈ 0.706
Therefore, the probability that a student has a sister given that they do not have a brother is approximately 0.706 or 70.6%.
In a class of students , the following data table summarizes how many students have a brother or a sister . What is the probability that a student has a sister given that they do not have a brother ? Has a brother Does not have a brother Has a sister 8 12 Does not have a sister 5
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