Question

There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. What is the probability that a randomly chosen team includes 4 or 6 boys?

A-0.12

B-0.37

C-0.49

D-0.75

Answer 1

There are 13 items and 10 are to be chose, so the number of combinations is 13C10 = (13!)/(3!)(10!) = 13x12x11/3x2x1 =
286 combinations. We want to know how many of those have 4 boys, thus all 6 girls. Getting 6 girls will be approximately
(6/13)(5/12)(4/11)(3/10)(2/9)(1/8) sampling without replacement
= 0.0006, which seems terribly small and seems to ignore the boys. Well, maybe some of this helps..

Answer 2

\[P(4\ boys)=\frac{\left(\begin{matrix}7 \\ 4\end{matrix}\right)\left(\begin{matrix}6 \\ 6\end{matrix}\right)}{\left(\begin{matrix}13 \\ 10\end{matrix}\right)}=0.1224\]
\[P(6\ boys)=\frac{\left(\begin{matrix}7 \\ 6\end{matrix}\right)\left(\begin{matrix}6 \\ 4\end{matrix}\right)}{\left(\begin{matrix}13 \\ 10\end{matrix}\right)}=0.3671\]
The probability that a randomly chosen team includes 4 or 6 boys is given by
P(4 boys) + P(6 boys) = 0.1224 + 0.3671 = 0.4895

Answer 3

If you round the above result to 2 decimal places, you can find the correct choice.

Answer 4

44 which is A