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

foass77W

foass77W

Answered question

2021-02-05

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

Answer & Explanation

FieniChoonin

FieniChoonin

Skilled2021-02-06Added 102 answers

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
=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(EF)=P(E)+P(F)P(EF).
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)
=n(freshman+n(female)n(freshman and female)n(S)
=18+15833=2533
Thus, the probability that a randomly selected student is a freshman or female is 2533.
Andre BalkonE

Andre BalkonE

Skilled2023-06-19Added 110 answers

To find the probability of the union of these two events, we can use the formula for the union of two events:
P(FFm)=P(F)+P(Fm)P(FFm)
Here, P(F) represents the probability of a student being a freshman, P(Fm) represents the probability of a student being female, and P(FFm) 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(Fm) 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)=Number of freshmenTotal number of students
Similarly, the probability of a student being female, denoted as P(Fm), can be calculated as the ratio of the number of females to the total number of students:
P(Fm)=Number of femalesTotal number of students
Finally, the probability of a student being both a freshman and female, denoted as P(FFm), 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(FFm)=Number of students who are both freshmen and femaleTotal 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(FFm)=P(F)+P(Fm)P(FFm)
xleb123

xleb123

Skilled2023-06-19Added 181 answers

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

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