Question

there are 10 people, 6 are boys and 4 are girls. what is the probability that, when a group of 5 are randomly chosen, that Kevin is chosen? please help, im stuck =(

Answer 1

let a be kevin, and bcdefghij be the less important kids

Answer 2

I can pick

abcde
acdef
adefg
aefgh
afghi
aghij

so 5 combinations that include kevin

Answer 3

so its 1 choose 1 times 9 choose 4 dividied by 10 choose 5?

Answer 4

arent there 6 with kevin?

Answer 5

I'm mistaken; there are more with kevin

Answer 6

i think if it is like i said it was, then it should be probability = 1/2 that it includes Mr. Kevin... right?

Answer 7

thinking too hard

Answer 8

5 is half of 10. the probability that "kevin" is chosen is
\[\frac{1}{2}\]

Answer 9

yep thats what i got too buddy =) you rule! ...

Answer 10

cuz its 1/10+1/10+1/10+1/10+1/10 = 5/10... which is one way to get there

Answer 11

you can use a bunch of formulas if you like, but they cloud the obvious

Answer 12

you could use
\[\frac{\dbinom{1}{1}\times \dbinom{9}{4}}{\dbinom{10}{5}}\]

Answer 13

or your could use
\[1-\frac{9}{10}\times \frac{8}{9}\times\frac{7}{8}\times \frac{6}{7}\times \frac{5}{6}\] that is one minus the probability that kevin is not chosen

Answer 14

but you are choosing half the people and therefore the probability that kevin is one of them is
\[\frac{1}{2}\] without any formulas