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 six times during the next seven weeks?

Answer 1

Firstly we need to find the probability of team C being selected at each draw.
The draw is sampling without replacement.
\[P(team\ C\ selected)=\frac{ \left(\begin{matrix}1 \\ 1\end{matrix}\right)\left(\begin{matrix}2 \\ 1\end{matrix}\right)}{\left(\begin{matrix}3 \\ 2\end{matrix}\right)}=\frac{2\times 2}{3\times 2}=\frac{?}{?}\]
When you have calculated the above value of probability, we can go to the next step which involves the binomial distribution.

Answer 2

the answer of that is 2/3

Answer 3

Now you need to use the binomial distribution to find the probability of team C being picked 7 times out of 7 draws.
\[P(7\ out\ of\ seven)= \left(\begin{matrix}7 \\ 7\end{matrix}\right)\times (\frac{2}{3})^{7}\times (\frac{1}{3})^{0}=(\frac{2}{3})^{7}=you\ can\ calculate\]
When you have calculated the probability of team C being picked 7 times out of 7 draws, subtract the probability value from 1 to find the answer.

Answer 4

this is what i got before subracting it by 1
0.05852766346

Answer 5

and this is what i got by subtracting it by 1 -0.94147233653 is that what u got as well?

Answer 6

The probability that team C is selected at least six times during the next seven weeks is 0.94. The answer is rounded.

Answer 7

You needed to subtract from 1:
1.0000000000000 - 0.05852766346 = 0.941472336 = 0.94 when rounded

Answer 8

0.9415 is four decimal places correct?

Answer 9

it said to round to four decimal places as needed:
what would that be ?

Answer 10

Yes, 0.9415 is the correct rounding.

Answer 11

Thats the wrong answer... Its supposed to be 0.2633