# The probability that a randomly selected student is a freshman or female

Question
Upper level algebra
The probability that a randomly selected student is a freshman or female

2021-02-06
Given:
There are 18 freshmen and 15 sophomores. Of the 18 freshmen, 10 are male, and of the 15 sophomores, 8 are male.
Formula used:
Probability for equally likely outcomes:
If an experiment has n equally likely outcomes, and if the number of ways in which an event E can occur is m, then the probability of E is,
P(E)= Number of ways that Ecan occur / Number of possible outcomes
$$=\frac{n(E)}{n(S)}$$
where, S is the sample space of the experiment.
Let E and F be the two events, then the probability of union of two events is,
$$P(E \cup F)=P(E)+P(F)-P(E \cap F)$$.
Calculation:
The total students in the college algebra is 33 students. That is, $$n(S) = 33$$.
The probability that a randomly selected student is a freshman or female is,
P (freshman or female) = P (freshman) + P (female) — P (freshman and female)
$$=\frac{n(freshman+n(female)-n(freshman\ and\ female)}{n(S)}$$
$$=\frac{18+15-8}{33} = \frac{25}{33}$$
Thus, the probability that a randomly selected student is a freshman or female is $$\frac{25}{33}$$.

### Relevant Questions

The probability that a randomly selected student is a sophomore or male.
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A table depicting the grade distribution for a college algebra class based on age and grade.
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A table depicting the grade distribution for a college algebra class based on age and grade.
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A table depicting the grade distribution for a college algebra class based on age and grade.
$$\begin{array} {lc} & \text{Gender} \ \text {Longer finger} & \begin{array}{l|c|r|r} & \text { Female } & \text { Male } & \text { Total } \\\hline \text { Index finger } & 78 & 45 & 123 \\\hline \text{ Ring finger } & 82 & 152 & 234 \\ \hline \text { Same length } & 52 & 43 & 95 \\ \hline \text { Total } & 212 & 240 & 452 \end{array}\ \end{array}$$