## IB Math Studies Conditional Probability

Number and algebra, Descriptive statistics, Logic, sets and probability, Statistical applications, Geometry and trigonometry, Mathematical models, Introduction to differential calculus.

### IB Math Studies Conditional Probability

IB Mathematical Studies SL – Probability, Conditional Probability

Can anyone help me with the following probability exercise?

“In a class of 27 students, 7 play football (F) and 18 play basketball (B). Three students play neither. ” One student is randomly selected from the class. What is the probability that the student plays football given that also plays basketball??”

Thanks
hill

Posts: 0
Joined: Tue Mar 19, 2013 8:49 pm

### Re: IB Math Studies Conditional Probability

IB Mathematical Studies SL – Probability, Conditional Probability

If you draw a Venn diagram and set x the number of students that play only football, y the number of students that play both, z the number of students that play only basketball then you will have the following equations

$x+y+z=27-3=24$ (1)

From the equation $x+y =7$ which are the students that play football, we have from (1) that $z=24-7=17$

From the equation $y+z =18$ which are the students that play basketball, we have from (1) that $y=18-17=1$ is the number of students that play both.

So, the required conditional probability is given by the following formula:

$P(F/B)=\frac{ P(F\cap B)}{P(B)}=\frac{1}{18}= \frac{1}{18}$

Hope these help!!
elizabeth

Posts: 0
Joined: Mon Jan 28, 2013 8:09 pm

### Re: IB Math Studies Conditional Probability

Thanks Elisabeth!!
hill

Posts: 0
Joined: Tue Mar 19, 2013 8:49 pm