To determine the probability that a teenager selected at random is female and their favorite hobby is watching films, follow these steps:
1. Identify the relevant quantities:
- The number of teenagers who are female and whose favorite hobby is watching films is 8.
- The total number of teenagers surveyed is 32.
2. Determine the probability:
- The probability of an event is given by the ratio of the favorable outcomes for the event to the total number of possible outcomes.
- In this context, the favorable outcomes are the number of female teenagers whose favorite hobby is watching films, and the total number of possible outcomes is the total number of teenagers surveyed.
Therefore, the probability (P) can be expressed as:
[tex]\[
P(\text{Female and Watching Films}) = \frac{\text{Number of females who watch films}}{\text{Total number of teenagers}}
\][/tex]
[tex]\[
P(\text{Female and Watching Films}) = \frac{8}{32}
\][/tex]
3. Simplify the fraction (if desired):
- To simplify [tex]\(\frac{8}{32}\)[/tex], divide both the numerator and the denominator by their greatest common divisor (GCD), which is 8.
[tex]\[
\frac{8 \div 8}{32 \div 8} = \frac{1}{4}
\][/tex]
Thus, the simplified probability is:
[tex]\[
P(\text{Female and Watching Films}) = \frac{1}{4}
\][/tex]
So, the probability that a randomly selected teenager is female and their favorite hobby is watching films is [tex]\(\frac{1}{4}\)[/tex].
