Chapter 13.5, Problem 11PPS

To determine

To determine probability that Brandi and Tisha draw each other’s names.

Answer to Problem 11PPS

Probability is $\frac{1}{306}.$

Explanation of Solution

If any event A does not affect the outcome of an event B, then event A and B are independent whereas if it affects then the events are dependent.

Here we can determine that the events are independent.

Total students = 18

Let us take event A= Brandi draw a name.

Now probability that she draws Tisha name is,

Hence P(A) = $\frac{1}{18}$

Similarly let even B= Tisha draw a name.

Probability that she draw Brandi name is,

(One name is already drawn so there are 17 left)

Hence P(B) = $\frac{1}{17}$

Therefore,

  $P\left(A\text{ and }B\right)=\frac{1}{18}\times \frac{1}{17}=\frac{1}{306}$