Question

A hockey team has 23 players on it consisting of 13 forwards, 7 defensemen, and 3 goalies. The team charity golf tournament is coming up and a team of 8 players is needed to play.
a) Determine the probability that 3 defensemen are selected to play in the tournament.
b) Determine the probability that at least one goalie will play in the tournament.
c) What is the expected number of forwards that will play in the tournament?

Answer 1

a) The required probability is given by:
\[P(3\ defensemen)=\frac{\left(\begin{matrix}7 \\ 3\end{matrix}\right)\left(\begin{matrix}16 \\ 5\end{matrix}\right)}{\left(\begin{matrix}23 \\ 8\end{matrix}\right)}\]

Answer 2

thnx so much

Answer 3

what about the other

Answer 4

b)
\[P(1\ goalie)=\frac{\left(\begin{matrix}3 \\ 1\end{matrix}\right)\left(\begin{matrix}20 \\ 7\end{matrix}\right)}{\left(\begin{matrix}23 \\ 8\end{matrix}\right)}\]
\[P(2\ goalies)=\frac{\left(\begin{matrix}3 \\ 2\end{matrix}\right)\left(\begin{matrix}20 \\ 6\end{matrix}\right)}{\left(\begin{matrix}23 \\ 8\end{matrix}\right)}\]
\[P(3\ goalies)=\frac{\left(\begin{matrix}3 \\ 3\end{matrix}\right)\left(\begin{matrix}20 \\ 5\end{matrix}\right)}{\left(\begin{matrix}23 \\ 8\end{matrix}\right)}\]
The probability of 1 or 2 or 3 goalies is the sum of the above 3 probabilities.

Answer 5

thnx for helping me
& c

Answer 6

c)
The expected number of forwards that will play is the average number of forwards that would be found using the results of a very large number of random selections of a team.
In this case the expected number number of forwards is found by using the following formula for the expected value of a discrete probability distribution.
\[E(X)=\sum_{}^{}xp(x)\]
The expected number of forwards is found with the following steps:
a) Calculate the probabilities of 1, 2, 3, 4, 5, 6, 7 and 8 forwards being selected.
b) Multiply each of the eight values of probability found in step a) by the coresponding number of forwards.
c) Add the 8 products found in step b)
{P(1) * 1} + {P(2) * 2} + ............................................. + {P(8) * 8} = expected number of forwards.

Answer 7

thnx so much dat's really helpful

Answer 8

i got 1.5 in step b it that right