Probability

[patricialec]

In a class with 50 student, 25 of the students are female, 15 of the students are mathematics majors, and 10 of the mathematics majors are female. If a student in the class is to be selected at random, what is the probability that the student selected will be female or a mathematics major or both?

 

[patricialec]

Ohh sorry guys...how would I begin to solve this problem :?: :roll: :roll: :roll:

 

[soroban]

Hello, patricialec!

We're expected to know this formula:

. . \(\displaystyle P(A \cup B) \;=\;P(A) + P(B) - P(A \cap B)\)

In a class with 50 student, 25 of the students are female, 15 of the students are mathematics majors,
and 10 of the mathematics majors are female.
If a student in the class is to be selected at random, what is the probability
that the student selected will be female or a mathematics major or both?

\(\displaystyle \text{We know that: }\;\begin{array}{ccccc}P(\text{female}) &=& \frac{25}{50} \\ \\[-3mm] P(\text{math}) &=& \frac{15}{50} \\ \\[-3mm] P(\text{female} \cap \text{math}) &=& \frac{10}{50} \end{array}\)


\(\displaystyle \text{Then: }\; P(\text{female} \;\cup \;\text{math}) \;=\;\underbrace{P(\text{female})}_{\frac{25}{50}} + \underbrace{P(\text{math})}_{\frac{15}{50}} - \underbrace{P(\text{female} \cap \text{math})}_{\frac{10}{50}} \;=\;\frac{30}{50} \;=\;\boxed{\frac{3}{5}}\)

 

[patricialec]

Thank you sooooo much for breaking that down for me. It really helps to put the problem in perspective. How did you do 3|5? as fraction on the computer?...