Question

Giving a test to a group of students, the grades and gender are summarized belowIf one student is chosen at random,Find the probability that the student was male OR got an "B".

Answer 1

ANSWER:

0.6875

STEP-BY-STEP EXPLANATION:

The first thing is to calculate the probability that the gender is male and also the probability that the grade is B, separately, like this:

$\begin{gathered} P(\text{male})=\frac{42}{80} \\ P(B)=\frac{19}{80} \end{gathered}$

Therefore, since it is the probability that it is male OR got and "B", it is the union of both events, and it would look like this:

$P(\text{male}\cup B)=P(male)+P(B)-P(male\cap B)$

Now, the intersection of both events would be the probability that he is a man and gets a B, it would look like this:

$P(male\cap B)=\frac{6}{80}$

We replace to be able to calculate the union, like this:

$\begin{gathered} P(\text{male}\cup B)=P(male)+P(B)-P(male\cap B) \\ P(\text{male}\cup B)=\frac{42}{80}+\frac{19}{80}-\frac{6}{80} \\ P(\text{male}\cup B)=\frac{55}{80}=\frac{11}{16}=0.6875 \end{gathered}$

The probability that the student was male OR got an "B" is 0.6875