1. ## probability questions

this is probability topic... give me solutions and explanations with this problem please...

1.) a person decides to take a vacation and has three places in mind : Las Vegas, the Bahamas , and Hawaii. She is twice as likely to go to Hawaii as to Las Vegas , and three times likely to go to Las Vegas as to the Bahamas . find the probability that she vacations in Las Vegas .

2. Bahamas: 10%
Las vegas: 30%
Hawaii: 60%

3. Hello, physicshelps!

A person decides to take a vacation and has three places in mind:
Las Vegas, the Bahamas , and Hawaii.
She is twice as likely to go to Hawaii as to Las Vegas,
and three times likely to go to Las Vegas as to the Bahamas.
Find the probability that she vacations in Las Vegas.
Let: . $\begin{array}{ccc}V &=& \text{prob. that she goes to Vegas} \\ B &=& \text{prob. that she goes to Bahamas} \\ H &=& \text{prob. that she goes to Hawaii} \end{array}$

It is certain that she will go to one of those three places: . $V + B + H \:=\:1$ .[1]

We are told that H is twice V: . $H \,=\,2V$ .[2]

We are told that V is three times B: . $V \,=\,3B$ .[3]

Substitute [3] into [2]: . $H \:=\:2V \:=\:2(3B) \quad\Rightarrow\quad H \:=\:6B$ .[4]

Substitute [3] and [4] into [1]:

. . $\begin{array}{c}V + B + H \:=\:1 \\ 3B + B + 6B \:=\:1 \\ 10B \:=\:1 \\ B \:=\:\frac{1}{10} \end{array}$

Substitute into [3]: . $V \:=\:3B \:=\:3\left(\tfrac{1}{10}\right) \:=\:\tfrac{3}{10}$

Therefore, the probability that she goes to Las Vegas is $\frac{3}{10}$.