# Probability question / venn diagram

Thanks

Among the 125 students in a sports association, 60 students are part of the basketball section (B), 45 students are part of the tennis section (T), and 25 students are part of both sections. Consider the following events: B: 'The student is part of the basketball section.' T: 'The student is part of the tennis section.' Create a Venn diagram representing the situation.

Calculate:

$$P(B)$$

$$P(T - B) = P(T \backslash B)$$

$$P(B ∪ T)$$

I think that there is an error in the statement, according to me the amount of student is 130 and not 125.

$$P(B) = \frac{85}{130} = \frac{17}{26} =65.38\%$$

$$P(T - B) = P(T \backslash B) =\frac{45}{130} =\frac{9}{26} = 34.61\%$$

$$P(B ∪ T) =$$

$$P (B \cap T) = P(B) . P(T)$$

$$P (B \cup T) = P(B) + P(T) - P (B \cap T)= 84 \%$$

• Why do you think the amount of students is 130? Feb 5 at 10:06
• Because 60 basketball students, 45 tennis and 25 both. Which ammounts to 130. Thats how i interpreted it @callculus42
– Wen
Feb 5 at 10:09
• Maybe 45 students are neither in the tennis team nor in the basketball team. Feb 5 at 10:11

You are misinterpreting the question.

60 students are part of the basketball section

It doesn't say they are part of the basket section only.

The $$25$$ students that are part of both sections are included in those $$65$$ (as well as in the $$45$$ in tennis section).

Make these adjustments and you will see why the number of students doesn't need to be $$130$$. Then your probability calculations should also be correct.

Also remember, some students (out of $$125$$) may not be in either of the groups.

Here's the Venn diagram representing the situation.