Question

In a class of 53 students, 11 have black hair, 20 have brown hair, 18 have blonde hair, and 4 have red hair. If one student is selected at random to put a problem on the board, find the odds against selecting a student with blonde hair.

Answer 1

The odds against selecting a student with blonde hair in a class of 53 students, where only 18 have blonde hair, are 35:18; this ratio represents the number of non-blonde to blonde-haired students.

Step-by-step explanation:

To find the odds against selecting a student with blonde hair, we calculate the ratio of the unfavorable outcomes to the favorable ones. In the class, there are 18 students with blonde hair (favorable outcomes), and the remaining students have hair that is not blonde (unfavorable outcomes).

The total number of students with non-blonde hair is 53 (total students in class) - 18 (students with blonde hair) = 35.

The odds against a student having blonde hair are therefore 35 (non-blonde hair students) to 18 (blonde hair students). This is often expressed as a ratio like 35:18, or simplified.

Steps to Simplify the Odds:

1. Count the total number of students who don't have blonde hair. That's 35 students.
2. Count the number of students who have blonde hair. That's 18 students.
3. Express these counts as a ratio, which is the odds against. So, the odds against are 35:18.

To further simplify, we can divide both numbers by their greatest common divisor if desired.