caitlyn calculated the probability of the complement of rolling a number greater than 2 on a 6 - side number…

caitlyn calculated the probability of the complement of rolling a number greater than 2 on a 6 - side number cube. she made her calculation as follows. p(less than or equal to 2): $\frac{numbers greater than 2}{numbers less than or equal to 2}=\frac{4}{2}$ did she make an error? explain.

caitlyn calculated the probability of the complement of rolling a number greater than 2 on a 6 - side number cube. she made her calculation as follows. p(less than or equal to 2): $\frac{numbers greater than 2}{numbers less than or equal to 2}=\frac{4}{2}$ did she make an error? explain.

Answer

Answer:

Yes, she made an error.

Explanation:

Step1: Identify total outcomes

A 6 - side number cube has 6 possible outcomes.

Step2: Find numbers less than or equal to 2

The numbers less than or equal to 2 on a 6 - side number cube are 1 and 2, so there are 2 such numbers.

Step3: Calculate probability

The probability $P(\text{less than or equal to }2)=\frac{\text{Numbers less than or equal to }2}{\text{Total numbers}}=\frac{2}{6}=\frac{1}{3}$, not $\frac{4}{2}$ as she calculated. She used the wrong ratio by dividing the number of numbers greater than 2 by the number of numbers less than or equal to 2 instead of dividing the number of numbers less than or equal to 2 by the total number of outcomes.