To determine the probability of opening a magazine to a page that is either page three or page seven, follow these steps:
1. Identify the Total Number of Possible Outcomes:
- The magazine contains a total of 14 pages. Therefore, if you open the magazine to a random page, there are 14 possible pages you could end up on.
2. Identify the Favorable Outcomes:
- The favorable outcomes are the pages we are interested in, which are specifically page three and page seven.
- Thus, the favorable outcomes are 2 (page three and page seven).
3. Calculate the Probability:
- Probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.
- So the probability [tex]\( P \)[/tex] is given by the formula [tex]\( P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} \)[/tex].
4. Putting the Values into the Formula:
- The number of favorable outcomes is 2.
- The total number of possible outcomes is 14.
- Therefore, the probability is [tex]\( P = \frac{2}{14} \)[/tex].
5. Simplify the Fraction:
- To simplify [tex]\( \frac{2}{14} \)[/tex], find the greatest common divisor (GCD) of 2 and 14, which is 2.
- Divide the numerator and the denominator by 2:
[tex]\[
\frac{2 \div 2}{14 \div 2} = \frac{1}{7}
\][/tex]
So, the probability of opening the magazine to a page that is either page three or page seven is [tex]\( \frac{1}{7} \)[/tex].
