Question

caitlyn calculated the probability of the complement of rolling a number greater than 2 on a 6 - sided number cube. she made her calculation as follows.
caitlyns work
p (less than or equal to 2) :
\\( \frac { \text { numbers greater than } 2 } { \text { numbers less than or equal to } 2 } = \frac { 4 } { 2 } \\)
did she make an error?
yes, the probability should be \\( \frac { 1 } { 2 } \\).
yes, the probability should be \\( \frac { 1 } { 3 } \\).
yes, the probability should be \\( \frac { 2 } { 3 } \\).
no, caitlins work is correct.

Explanation:

Step1: Determine the sample space

A 6 - sided cube has numbers \(1,2,3,4,5,6\). So the sample space \(n(S)=6\).

Step2: Find the number of elements in the complement event

The complement of "rolling a number greater than 2" is "rolling a number less than or equal to 2". The numbers less than or equal to 2 are \(1\) and \(2\), so \(n(A) = 2\).

Step3: Calculate the probability

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\). Substituting the values, we get \(P(A)=\frac{2}{6}=\frac{1}{3}\).

Answer:

Yes, the probability should be \(\frac{1}{3}\).