# Math Help - need urgent help

1. ## need urgent help

Out of 200 students, 113 are on the honor roll or on a sports team. 80 students are on the honor roll, and 72 students are on a sports team. What is the probability that a student is chosen out of the 200 students who is on the honor roll and a sports team?

2. Hello, IronMan21!

Out of 200 students, 113 are on the honor roll or on a sports team.
80 students are on the honor roll, and 72 students are on a sports team.
What is the probability that a student is chosen out of the 200 students
who is on the honor roll and a sports team?
Are you familiar with this formula? . $P(A \cup B) \;=\;P(A) + P(B) - P(A \cap B)$

Let . $\begin{array}{ccc}H &=&\text{on Honor Roll} \\ S &=& \text{on Sports team}\end{array}$

We are told that: . $P(H \cup S) = \tfrac{113}{200},\;P(H) = \tfrac{80}{200},\;P(S) = \tfrac{72}{200}$

$\text{So we have: }\;\underbrace{P(H \cup S)}_{\frac{113}{200}} \;=\;\underbrace{P(H)}_{\frac{80}{200}} + \underbrace{P(S)}_{\frac{72}{200}} - P(H \cap S)$

Therefore: . $P(H \cap S) \;=\;\tfrac{80}{200} + \tfrac{72}{200} - \tfrac{113}{200} \;=\;\boxed{\frac{39}{200}}$

3. thanks soroban!