Please check and please help!

[krisolaw]

In the game of KENO, 80 numbers are displayed on a reader board. Twenty of thse numbers are chosen to be the winning numbers. Suppose a person has selected 10 numbers on a playing card. What is the probability of selecting exactly 6 correct numbers?

Here is what I get:

P(6 correct)= (10C6)/(80C20) = 5.94 x 10^-17

Thanks in advance!

The second problem I am having a bit of trouble setting up.

There are 30 people in your speech class. For the last 10 days of the quarter, 3 students are randomly selected to give their final speech for the quarter. If you were not selected to give your speech during the first 5 days, what is the probability that you will be selected to give it on the 6th day?

Thanks again in advance!

 

[Unco]

In the game of KENO, 80 numbers are displayed on a reader board. Twenty of thse numbers are chosen to be the winning numbers. Suppose a person has selected 10 numbers on a playing card. What is the probability of selecting exactly 6 correct numbers?

Here is what I get:

P(6 correct)= (10C6)/(80C20) = 5.94 x 10^-17

hmm...
The probability of a number being correct = 20/80 = 1/4, agreed?

It becomes a binomial problem. Number of trials: 10, pi = 1/4.

P(X=6) = 10C6 * 0.25^6 * 0.75^4 etc.

Is this familiar?

 

[Unco]

I'm having difficulty with the second one. It could be that I'm misreading it (VERY possible), but are we to assume they each make speeches on seperate nights?

 

[soroban]

Hello, krisolaw!

"Separate nights" . . . Where are you getting that?
I reworded the problem to emphasize my interpretation.

There are 30 people in your speech class.
During each of the last 10 days of the course, 3 students are randomly selected to give their final speech.
If you were not selected to give your speech during the first 5 days,
what is the probability that you will be selected to give it on the 6th day?

On each day, three students give their final speeches. .They are not chosen again.

During the first five days, 15 (other) students gave their final speeches.

On the sixth day, there are 15 students to choose from, including you.

The probability of being picked is \(\displaystyle \frac{1}{15}\)

There are \(\displaystyle 3\) chances to draw your name.

Answer: .\(\displaystyle 3\,\times\,\frac{1}{15}\;=\;\frac{1}{5}\)