Question

The students in a small class are divided into three teams A, B and C. Each week two of the teams are selected at random to participate in a competition. What is the probability that team C is selected at least two times during the next three weeks?

Answer 1

The probability that team C is selected in a random draw is given by
\[P(team\ C\ selected)=\frac{\left(\begin{matrix}1 \\ 1\end{matrix}\right)\left(\begin{matrix}2 \\ 1\end{matrix}\right)}{\left(\begin{matrix}3 \\ 2\end{matrix}\right)}=\frac{2}{3}\]
Now we have the probability of team C being selected, the probability that team C is selected at least two times during the next three weeks can be found from the binomial distribution. Do you know how to continue from here?

Answer 2

Not really :( I read the answer similar to this one that you posted but I still don't get it!

Answer 3

We can use the binomial distribution to find the probability of team C being selected 3 times during the next 3 weeks as follows:
\[P(selected\ 3\ out\ of\ 3)=\left(\begin{matrix}3 \\ 3\end{matrix}\right)\times (\frac{2}{3})^{3}\times (\frac{1}{3})^{0}=(\frac{2}{3})^{3}=you\ can\ calculate\]
When you have calculated that probability, subtract it from 1 to find the required probability.

Answer 4

@HelpMeWithMath5 Are you there?

Answer 5

Yes thank you! the answer I got was 0.7037, but when I entered that answer into the online program for one of my assignments, it says its wrong :S

Answer 6

How many decimal places were required for the answer?

Answer 7

4 decimal places

Answer 8

Sorry, my bad. I did not read the question carefully enough.
To get the correct answer the probabilities of two selections and 3 selections must be added.
\[P(selected\ 2\ out\ of\ 3)=\left(\begin{matrix}3 \\ 2\end{matrix}\right) \times (\frac{2}{3})^{2}\times (\frac{1}{3})=3\times (\frac{2}{3})^{2}\times (\frac{1}{3})=you\ can\ calculate\]

Answer 9

@HelpMeWithMath5 How are you doing?

Answer 10

Wow something happened to my computer and it automatically sent in nothing as an answer and that was my final try, A message popped up and said the answer was 0.7407!!! This is very strange

Answer 11

But thank you anyway!!!

Answer 12

The correct answer is indeed 0.7407
P(2 out of 3) + P(3 out of 3) = 0.444444444 + 0.296296296

Answer 13

Yes I got that, I just emailed my teacher the answer and she is gonna fix my score. Thanks for the help!

Answer 14

You're welcome :)