Question

The 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. Given that a student earns a B on the first exam, what is the probability that the student does NOT earn a C on the second exam?

A1 B1 C1
A2 2 7 1
B2 2 10 3
C2 1 3 1

Answer 1

17/20 = 85%

Explanation:

Of the students who earned a B on the first exam (in other words, looking only at the B₁ column), 7 got As on the second exam, 10 got Bs on the second exam, and 3 got Cs on the second exam.

The total number of students who got a B on the first exam is:

7 + 10 + 3 = 20

Of those students, the number that did NOT get a C on the second exam is:

7 + 10 = 17

So the probability is 17/20, or 85%.

Answer 2

17/20 = 85%

Explanation:

`\left[\begin{array}{cccc} &A_1&B_1&C_1\\A_2&2&7&1\\B_2&2&10&3\\C_2&1&3&1\end{array}\right]`

Of the students who earned a B on the first exam (in other words, looking only at the B₁ column), 7 got As on the second exam, 10 got Bs on the second exam, and 3 got Cs on the second exam.

The total number of students who got a B on the first exam is:

7 + 10 + 3 = 20

Of those students, the number that did NOT get a C on the second exam is:

7 + 10 = 17

So the probability is 17/20, or 85%.