foass77W

2021-02-05

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

FieniChoonin

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
$=\frac{n\left(E\right)}{n\left(S\right)}$
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,
$P\left(E\cup F\right)=P\left(E\right)+P\left(F\right)-P\left(E\cap F\right)$.
Calculation:
The total students in the college algebra is 33 students. That is, $n\left(S\right)=33$.
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)

$=\frac{18+15-8}{33}=\frac{25}{33}$
Thus, the probability that a randomly selected student is a freshman or female is $\frac{25}{33}$.

Andre BalkonE

To find the probability of the union of these two events, we can use the formula for the union of two events:
$P\left(F\cup Fm\right)=P\left(F\right)+P\left(Fm\right)-P\left(F\cap Fm\right)$
Here, $P\left(F\right)$ represents the probability of a student being a freshman, $P\left(Fm\right)$ represents the probability of a student being female, and $P\left(F\cap Fm\right)$ 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 $P\left(F\right)$ be the probability of a student being a freshman and $P\left(Fm\right)$ be the probability of a student being female.
The probability of a student being a freshman, denoted as $P\left(F\right)$, can be calculated as the ratio of the number of freshmen to the total number of students:

Similarly, the probability of a student being female, denoted as $P\left(Fm\right)$, can be calculated as the ratio of the number of females to the total number of students:

Finally, the probability of a student being both a freshman and female, denoted as $P\left(F\cap Fm\right)$, can also be calculated using the ratio of the number of students who are both freshmen and female to the 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:
$P\left(F\cup Fm\right)=P\left(F\right)+P\left(Fm\right)-P\left(F\cap Fm\right)$

xleb123

The probability of the union of two events can be found using the formula:
$P\left(F\cup Fm\right)=P\left(F\right)+P\left(Fm\right)-P\left(F\cap Fm\right)$
Here, $P\left(F\right)$ represents the probability that a student is a freshman, $P\left(Fm\right)$ represents the probability that a student is female, and $P\left(F\cap Fm\right)$ represents the probability that a student is both a freshman and female.

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