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

Question

FieniChoonin · Accepted Answer

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 (f r e s h m a n + n (f e m a l e) - n (f r e s h m a n a n d f e m a l e)}{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}

.

Andre BalkonE · Accepted Answer

To find the probability of the union of these two events, we can use the formula for the union of two events:

P (F \cup F m) = P (F) + P (F m) - P (F \cap F m)

Here,

P (F)

represents the probability of a student being a freshman,

P (F m)

represents the probability of a student being female, and

P (F \cap F m)

represents the probability of a student being both a freshman and female.
Assuming that these events are independent (i.e., being a freshman does not affect the likelihood of being female and vice versa), we can calculate the probabilities individually.
Let

P (F)

be the probability of a student being a freshman and

P (F m)

be the probability of a student being female.
The probability of a student being a freshman, denoted as

P (F)

, can be calculated as the ratio of the number of freshmen to the total number of students:

P (F) = \frac{Number of freshmen}{Total number of students}

Similarly, the probability of a student being female, denoted as

P (F m)

, can be calculated as the ratio of the number of females to the total number of students:

P (F m) = \frac{Number of females}{Total number of students}

Finally, the probability of a student being both a freshman and female, denoted as

P (F \cap F m)

, can also be calculated using the ratio of the number of students who are both freshmen and female to the total number of students:

P (F \cap F m) = \frac{Number of students who are both freshmen and female}{Total number of students}

Substituting these values back into the formula for the union of events, we can find the probability that a randomly selected student is a freshman or female: