The probability the student earns a B on the second exam, given that a student earns a B on the first exam is 0.5 or 50%.
Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
The below table shows the number of students in a class that received letter grades on 2 recent exams.
The first exam is shown across the top and is summarized as A1, B1, and C1, and the second exam is in the first column, A2, B2, and C2. In the given table, the student get B in first exam is,
[tex]X=(7+10+3)\\X=20[/tex]
The student get B in second exam is which got B in first exam are 10.
[tex]Y=10[/tex]
The total number of students are,
[tex]2+2+1+7+10+3+1+3+1=30[/tex]
The probability the student earns a B on the second exam, given that a student earns a B on the first exam, is,
[tex]P(Y|X)=\dfrac{P(Y\cap X)}{P(X)}\\P(Y|X)=\dfrac{\dfrac{10}{30}}{\dfrac{20}{30}}\\P(Y|X)=0.5[/tex]
Thus, the probability the student earns a B on the second exam, given that a student earns a B on the first exam, is 0.5 or 50%.
Learn more about the probability here;
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