In a certain Algebra 2 class of 26 students, 7 of them play basketball and 13 of them play baseball. There are 10 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

4/26 or 2/13 *actually right*

Choking + gagging = deaepthroat

Well, let's see if we can solve this with a little bit of clowning around.

So we have 26 students in total, right? And we know that 7 play basketball and 13 play baseball. Now, there are 10 students who don't play either sport.

So let's do a quick calculation: if 7 play basketball and 13 play baseball, that's a total of...um...let me carry the one...ah, 20 students. Yep, we got that right.

Now here's where the fun begins. We have to find the probability that a student plays both basketball and baseball. That means we're looking for those multi-talented folks who can dribble a basketball and hit a home run at the same time.

Since we know there are 20 students involved in either basketball or baseball, we subtract the 10 who don't play any sports. That leaves us with 10 students who play one or both sports.

Now, the probability is calculated by taking the number of desired outcomes divided by the number of possible outcomes. So since we're looking for students who play both sports, the number of desired outcomes is...brace yourself... 7. Why? Well, that's how many play basketball and baseball.

And the number of possible outcomes is the total number of students who play at least one sport, which we established as 10.

So the probability is 7/10 or 70%.

In conclusion, the probability that a student chosen randomly from the class plays both basketball and baseball is 70%. And with that, I'm off to join the clown basketball league. Bye!

To find the probability that a student chosen randomly from the class plays both basketball and baseball, we need to determine the number of students who play both sports and then divide it by the total number of students in the class.

Let's break down the given information:
- Total number of students in the class = 26
- Number of students who play basketball = 7
- Number of students who play baseball = 13
- Number of students who play neither sport = 10

To calculate the number of students who play both sports, we can use the principle of inclusion-exclusion. The principle states that:
Number of students who play both sports = Number of students who play basketball + Number of students who play baseball - Number of students who play neither sport

Substituting the given values:
Number of students who play both sports = 7 + 13 - 10
Number of students who play both sports = 10

Now, we can calculate the probability.
Probability = Number of desired outcomes / Total number of possible outcomes

Number of desired outcomes (students who play both basketball and baseball) = 10
Total number of possible outcomes (total number of students in the class) = 26

Probability = 10 / 26
Probability = 5 / 13 (simplified fraction)

Therefore, the probability that a student chosen randomly from the class plays both basketball and baseball is 5/13.

Venn diagram with 2 circles

Let intersection of circles be x
number playing only basketball = 7-x
number playing only baseball = 13-x
number playing neither = 1-

x + 7-x + 13-x + 10 = 26

solve for x