Question

L

5.6.3 Toat(CST): Applications of Probability
This Venn diagram shows sports played by 10 students.
PLAYS
BASKETBALL
PLAYS
SOCCER
Jada
Gabby
Fran
Ella
Mai
Mickey
Marcus
lan
MEDICOLE
Karl
Juan
Let event A = The student plays basketball.
Let event B = The student plays soccer.
What is P(AB)?​

Answer 1

The question is shown in the picture attached

Answer:

• P(A or B) = 7/10

Step-by-step explanation:

1. Find the elements that belong to the event A: The student plays basketball.

These are represented by the names inside the blue circle:

• Fran, Juan, Illan, and Ella. Thus there are four possible outcomes for this event.

2. Find the elements that belong to the event B: The student plays soccer.

These are represented by the names inside the red circle:

• Mickey, Mai, Marcus, Ian, and Ellan. Those are five possible outcomes.

3. Find the elements that play both sports:

Those are the elements in the intersection of both circles: Iand and Ella.

Then, those are two elements.

4. Find the Universe of students.

These are 10 students: Karl, Jada, Gabby (who do not play either basketball or soccer), Fran, Juan, Ian, Ella, Michey, Mai, and Marcus.

5. You want to determine P (A or B).

That is the probability that a student plays basketball or soccer.

Using probability simbology:

• P (A or B) = P(A∪B) = P(A) + P(B) - P(A∩B)

• P(A) = 4/10 = 2/5

• P(B) = 5/10 = 1/2

• P(A∩B) = 2/10 = 1/5

• P(A or B) = 2/5 + 1/2 - 1/5 = 7/10