Question

Problem 9

Answer 1

I can't figure out the 3rd blank. Help?

Answer 2

I was thinking .5*.5*5 or .5+.5*1 but those arent right....

Answer 3

@antoni7 @Directrix @satellite73

Answer 4

if you guys can't open the file, i can make it a PDF :)

Answer 5

is it the "at least once" part?

Answer 6

it is not clear to me, but it looks like that is the part you missed

Answer 7

yeah

Answer 8

sorry!

Answer 9

ok it is easiest to compute the probability that it does not happen at all

Answer 10

that would be \(.5\times .5=.25\)

Answer 11

so it that is the probability it does not happen at all, then the probability it happens "at least once" meaning not never is \(1-.25=.75\)

Answer 12

so 1-.25

Answer 13

yup

Answer 14

ah you're so awesome! :D

Answer 15

(blush)

Answer 16

could you help me with one last problem?

Answer 17

sure if i can

Answer 18

With this one I have no idea how to do

Answer 19

yeah because it is a pain

Answer 20

o ok. i thought i was just being slow like usual. lol

Answer 21

at least two fours means two or three since you are only dealt 3 cards

Answer 22

the probability you are dealt exactly two fours is
\[\frac{\binom{4}{2}\binom{28}{1}}{\binom{32}{3}}\] which is actually not that bad

Answer 23

two out of the 4 fours, number of ways to do that is \(\frac{4\times 3}{2}=6\) and one out of the other cards is \(28\) so the numerator is \(6\times 28\) and the denominator is
\[\binom{32}{3}=\frac{32\times 31\times 30}{3\times 2}=4660\]

Answer 24

then you have to do it with 3 fours, which is actually easier
it is \[\frac{\binom{4}{3}}{\binom{32}{3}}=\frac{4}{4660}\]

Answer 25

then you have to add them
\[\frac{6\times 28}{4660}+\frac{4}{4660}\] i would use a calculator, although you don't really need one

Answer 26

how we doing so far?

Answer 27

hold on, let me process everything

Answer 28

you can keep going though

Answer 29

ok, so i get .0369098712

Answer 30

i get this
http://www.wolframalpha.com/input/?i= \frac{6\times+28}{4660}%2B\frac{4}{4660}

Answer 31

yeah it is the same

Answer 32

for the next one we have some more work to do

Answer 33

ok so whats the final answer to part 1? that doesnt seem to be correct

Answer 34

no?

Answer 35

let me read again carefully

Answer 36

http://www.wolframalpha.com/input/?i=%286*28%29%2F%2832+choose+3%29%2B4%2F%2832+choose+3%29

Answer 37

do you want me to show you an example problem that is similar to this and has the answers? it doesnt show work though

Answer 38

try that one

Answer 39

i must have made some arithmetic error, because it is slightly different than the last answer

Answer 40

yeah, that's right!

Answer 41

okay good

Answer 42

now for the last one lets try to cheat

Answer 43

can't we just subtract from 1?

Answer 44

no the compliment is a very complicated set

Answer 45

yeah, ok. nevermind.

Answer 46

pick a card, it has to be some number with probability 1
pick another , there are 28 different cards out of 31 to choose that are different from the first one
pick a third, there are now 26 out of 30 different from the first two
try
\[\frac{28}{31}\times \frac{26}{30}\] and see if it works

Answer 47

oh no that is wrong, try
\[\frac{28}{31}\times \frac{24}{30}\] the 26 was a mistake

Answer 48

i get .7827956989 and that's incorrect

Answer 49

try this
http://www.wolframalpha.com/input/?i= \frac{28}{31}\times+\frac{24}{30}

Answer 50

http://www.wolframalpha.com/input/?i=28%2F31*24%2F30

Answer 51

Yeah! That's correct! Thanks mane! :)

Answer 52

i wrote 26 and that is not right, 24 should be right my mistake