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 brother given that they have a sister?
Has a brother Does not have a brother
Has a sister 2 3
Does not have a sister 4 13
There are a total of 22 students in the class. Out of these, 2 have both a brother and a sister, and 4 have neither a brother nor a sister. So, there are 16 students who have either a brother or a sister.
Out of these 16, 2 have both a brother and a sister. So, there are 14 students who have either a brother or a sister but not both.
Out of these 14, 2 have a sister and a brother, so there are 12 students who have a sister but not a brother.
Therefore, the probability that a student has a brother given that they have a sister is 0, as none of the students who have a sister also have a brother.
In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student who passed the test completed the homework?
Passed the test Failed the test
Completed the homework 19. 2
Did not complete the homework 3 6
To find the probability that a student has a brother given that they have a sister, we can use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
In this case, let's define event A as "student has a brother" and event B as "student has a sister".
From the data table, we see that there are 2 students who have both a brother and a sister. Therefore, P(A and B) = 2.
The total number of students who have a sister is given by the sum of the two entries in the "Has a sister" row: 2 + 3 = 5. Therefore, P(B) = 5.
Plugging these values into the formula for conditional probability:
P(A|B) = P(A and B) / P(B) = 2 / 5
Therefore, the probability that a student has a brother given that they have a sister is 2/5 or 0.4.
To find the probability that a student has a brother given that they have a sister, we need to use conditional probability.
Conditional probability is calculated using the formula:
P(A|B) = P(A ∩ B) / P(B)
Where P(A|B) represents the probability of event A occurring given that event B has already occurred, P(A ∩ B) represents the probability of both events A and B occurring together, and P(B) represents the probability of event B occurring.
In this case, event A is the student having a brother, and event B is the student having a sister.
Looking at the data table, we see that there are 2 students who have both a brother and a sister. This represents the probability of both events A and B occurring together, P(A ∩ B).
The total number of students who have a sister is 2 + 3 = 5. This represents the probability of event B occurring, P(B).
So, the probability that a student has a brother given that they have a sister, P(A|B), can be calculated as:
P(A|B) = P(A ∩ B) / P(B) = 2/5
Therefore, the probability that a student has a brother given that they have a sister is 2/5 or 0.4.