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 \(\frac{25}{33}\).

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 \(\frac{25}{33}\).