Question

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

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 $$\frac{25}{33}$$.