Math Help - Probability problem

1. Probability problem

Hi
First of all i would like to apologize for my bad english. I hope you understand me.

a lot of bikes are parked in front of a university. A truck unfortunately hits 10 bikes and destroy them.

of the students at the university: 20% are smoker, 40% are bikers, 25 % of the bikers are smokers.

what´s the probability that none of the 10 bikes belongs to the smokers??

It seems to me that we need more informations to solve this question?? or what?? Hope you can help

Thanks

2. Re: Probability problem

Hello, Jonas8000!

A lot of bikes are parked in front of a university.
A truck unfortunately hits 10 bikes and destroy them.

Of the students at the university: 20% are smoker, 40% are bikers, 25 % of the bikers are smokers.

What is the probability that none of the 10 bikes belongs to the smokers??

We can place the given information in a chart.

$\begin{array}{c|c|c|c|}& \text{Biker} & \sim\text{Biker} & \text{Total} \\ \hline \text{Smoker}&10\%&&20\% \\ \hline \sim\text{Smoker} &&& \\ \hline \text{Total} & 40\% && 100\% \\ \hline \end{array}$

We can supply the missing information.

$\begin{array}{c|c|c|c|}& \text{Biker} & \sim\text{Biker} & \text{Total} \\ \hline \text{Smoker}&10\%&10\%&20\% \\ \hline \sim\text{Smoker} &30\%&50\%&80\% \\ \hline \text{Total} & 40\% &60\%& 100\% \\ \hline \end{array}$

Now you can answer the question.

3. Re: Probability problem

Since 25% of the bikers are smokers, the probability that a bike chosen at random belongs to a non-smoker is 0.75. So the probability that all 10 bikes belong to non-smokers is 0.75^10, which is about 0.0563.

The problem statement is tricky; it contains more information than is needed to solve the problem.