Question

At the start of the school year, students in Mr. Pi’s class were asked the

Answer 1

Answer:

• No, there is not enough information to determine how many students were absent that particular morning.

Explanation:

The probability of randomly selecting a student who answered the question “yes” is the number of students that responded yes divided by the number of students present. Thus, it was:

• 21/30 = 7/10

The probability of randomly selecting a student who answered the question “no” is the number of students who answered "no" divided by the number of students present. Thus, it was:

• 9/30 = 3/10

On one particular morning later in the year, the probability of randomly selecting a student who had answered the question “yes” was 3/4

The equivalent ratios to 3/4 will tell you the possible combinations of students that answered yes and students present on that particular morning.

For instance: 3/4 = 6/8

• 6/8 would mean that there were 6 students that answered yes and 8 total students on that particular morning.

Since more than half of class was present, the total number of students was greater than 15. Then, you must find a ratio with a denominator greater than 15 (and less than 30).

The other equivalent ratios to 3/4 are: 9/12, 12/16, 15/20, 18/24, 21/28, 24/32, ...

That means that the only possibilities with more than 15 and less than 30 present students are 12/16, 15/20, 18/24, and 21/28.

The total number of absents might have been:

• 30 - 28 = 2
• 30 - 24 = 6
• 30 - 20 = 10
• 30 - 16 = 14

Since at least one of the students who had answered “yes” was absent and at least one of the students who had answered “no” was absent, all the above possibilities are valid: there is not enough information to determine how many students were absent that particular morning; they could be 2, 6, 10, or 14.