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

0.6875

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})=(42)/(80) \\ P(B)=(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)=(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)=(42)/(80)+(19)/(80)-(6)/(80) \\ P(\text{male}\cup B)=(55)/(80)=(11)/(16)=0.6875 \end{gathered}`

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