Question

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

Upper level algebra
ANSWERED
asked 2021-02-05
The probability that a randomly selected student is a freshman or female

Expert Answers (1)

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