SOLUTION: 12 boys and 10 girls in which seven students are chosen to go to the blackboard. What is the probability that at least 2 girls are chosen? C(22,7) = 170,544 I know the answer

Question 368929: 12 boys and 10 girls in which seven students are chosen to go to the blackboard. What is the probability that at least 2 girls are chosen?
C(22,7) = 170,544
I know the answer to this one is 16/17 but how?
I did the long way, need the short way
Long way:
7 b 0g C(12,7) * C(10,0) = 792
6 b 1g C(12,6) * C(10,1) = 9,240
etc...
How do I do the answer in the below format:
C(#,#) C(#,#)
-------------
C(22,7)
A question that relates to the above:
What is the probability that no boys are chosen?
What is the probability that more boys than girls are chosen?
What is the probability that the first three children chosen are boys?

Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
12 boys and 10 girls in which seven students are chosen to go to the blackboard. What is the probability that at least 2 girls are chosen?

 
1 - (probability of that NOT happening)  =
 
1 - (the probability that all 7 were boys) - (the probability that there was one girl and 6 boys) =

What is the probability that no boys are chosen?

 
That is the same as all girls are chosen, or

What is the probability that more boys than girls are chosen?

 
There isn't any shortcut to this:
 
P(7boys,0girls) + P(6 boys, 1 girl) + P(5 boys, 2 girls) + P(4 boys, 3 girls)

What is the probability that the first three children chosen are boys?

 
Choose the first three any 3 of the 12 boys C(12,3) ways, and the other 4 any
of the remaining 19 students, C(19,4), so the probability is



Edwin

RELATED QUESTIONS
In a class containing 10 boys and 8 girls 5 students are chosen (a)what is the... (answered by Jeff Gordon)

In a classroom of 9 boys and 14 girls, seven students are chosen to present their seven... (answered by ewatrrr)

Mr. Larsen's third grade class has 22 students, 12 girls and 10 boys. Two students must... (answered by stanbon)

Two students from a class of 12 boys and 8 girls are chosen at random. What is the... (answered by FrankM)

In a class of 40 students, 14 of which are girls, 6 students are to be selected at... (answered by ewatrrr)

In a class, there are 15 girls and 13 boys. Three students are chosen at random to form a (answered by Boreal)

At Med U. the failure rate is 20%. Of 15 students registered in the freshman class;... (answered by ewatrrr)

Two students are to be selected at random from a class with 10 girls and 12 boys. What is (answered by ikleyn)

in a class of 10 students, there are 4 boys and 6 girls. If a committee of 5 students is... (answered by stanbon)