A group of freshmen at a local university consider joining the equestrian team. Thirty-five percent of students choose Western riding, 45% choose dressage, and 50% choose jumping. Twenty percent choose both dressage and jumping, while 10% choose Western and dressage. No one chooses Western and jumping. There are no horses suitable for two styles, and each student is assigned to one horse. If two students decide to join the team, what is the probability that both are Western and dressage riders, if they independently decide?
A)0.1
B)0.2
C)0.01
D)0.8

Question

Quizplus · Accepted Answer

Let's first make a Venn diagram to illustrate the given information:

```
              Dressage
              /      \
             /        \
            /          \
    Western----20%----Other
            \          /
             \        /
              \      /
              Jumping
```

From the diagram, we can see that 10% of students choose both Western and dressage. Therefore, the probability that any one student is both Western and dressage is 0.1.

To find the probability that two randomly chosen students are both Western and dressage riders, we need to multiply the probabilities of each event. Since the choices of the two students are independent, we can multiply probabilities.

So, the probability that the first student is Western and dressage is 0.1, and the probability that the second student is also Western and dressage is also 0.1 (assuming replacement). Therefore, the probability that both students are Western and dressage riders is:

0.1 x 0.1 =0.01

Therefore, the answer is C (0.01).

A Group of Freshmen at a Local University Consider Joining