In a hat are 200 numbers -- each of the numbers 1 through 25 occurs 8 times. You pick three numbers from the hat without replacement. What is the probability that all three of the numbers are 25?
2006-07-26 21:02:35 · 12 answers · asked by Lennon TheNewsBassist 1 in Science & Mathematics ➔ Mathematics
1 out of every 8...dont really know never was good at that math thing.
2006-07-26 21:07:01 · answer #1 · answered by ? 5 · 0⤊ 1⤋
Probability that the 1st number is 25:
8/200 = 1/25
Probability that the 2nd number is 25
7/199 (since there are only 7 25's left and 199 numbers left)
Probability that the 3rd number is 25:
6/198 = 1/33
Probability that all 3 numbers are 25
1/25 · 7/199 · 1/33
= 7/164175
^_^
2006-07-27 07:34:43 · answer #2 · answered by kevin! 5 · 0⤊ 0⤋
8*7*6/(200*199*198)
Basically, the probability of something occuring is the number of ways that the desired outcome can occur over the number of total possible outcomes. So, for your case the number of ways that you can pick the number 25, there's 8 ways to pick the first 25 then there's 7 (because you already took one) and on the last step there's 6. So, the total number of ways you can pick three 25's is 8*7*6. The same follows for the denominator.
2006-07-27 04:11:05 · answer #3 · answered by craizdwei 2 · 0⤊ 0⤋
Well, the chance of you picking 25 the first time is 8 in 200, the second time is 7 in 199, the third time is 6 in 198. Multiply them all together, the probability is 336 out of 7880400. Factor it down to 7 in 164175, and its pretty freaking small.
2006-07-27 04:08:16 · answer #4 · answered by Joecuki 2 · 0⤊ 0⤋
1:25
2006-07-27 06:07:11 · answer #5 · answered by Ultimate Chopin Fan 4 · 0⤊ 0⤋
8/200 x 7/199 x 6/198
= 0.0000426
2006-07-27 04:07:44 · answer #6 · answered by Vanguard 3 · 1⤊ 0⤋
There are 4 "good" numbers (25) and 196 "bad" numbers. The probability of picking 3 out of 4 and 1 out of 196 is
[C(4,3) * C(196,1)] / C(200,4)
=
[4 * 196] / 64684950
=
0.00001212
Note: C(n,r) is the binomial coefficient
2006-07-27 04:07:26 · answer #7 · answered by dutch_prof 4 · 0⤊ 0⤋
=3/200*2/199*1/198
2006-07-27 05:36:36 · answer #8 · answered by budweiser 2 · 0⤊ 0⤋
The odds are 1 in 15,625. Reason? 25 x 25 x 25 = 15,625.
2006-07-27 04:45:32 · answer #9 · answered by Math_Maestro 7 · 0⤊ 0⤋
I might be wrong, but, depending on how you pick them (if you pick them all at the same time), it should be a .000064 chance they will all three be 25) [ it would be .04 X .04 X .04 ]
64 chances in a million, or one chance in 15,625
2006-07-27 04:12:29 · answer #10 · answered by Wayne A 5 · 0⤊ 0⤋
I haven't tried this kind of problem in a long time...
1:100
2006-07-27 04:07:22 · answer #11 · answered by I'm awesome! 3 · 0⤊ 0⤋