I have 462 ping-pong balls. 167 of them are red. If I choose 7 of them, without replacement (i.e. I don't put them back after choosing), what is the probability that all 7 are red? How do I solve this?
Thank you in advance!
Thanks everyone for replying so quickly! I'll give the points (once the time limit lets me) to Hauk who answered with details first, but I appreciate everyone's help. Cheers.
Hayk
Favorite Answer
The chance that your first ball is red is 167/462
Assuming you get a red ball, now one red ball is out of the ball pile. So the chance you'll get a red ball for the second one is 166/461.
You do this 7 times and since you want all 7 in a row to be red, you have to multiply the fractions.
167/462x166/461x165/460x164/459x163/458x162/457x161/456= 3.19x10^15/ 4.29x10^18=7.4x10^-4=.00074
So the chances of that happening are .00074 or .07%.
cryptogramcorner
On the first pick you have a 167/462 chance of picking a red one. If you get one, then you
have a 166/461 chance of getting a red ball on the 2nd pick.
Then you have a 165/460 chance of getting red on the 3rd pick, etc.
These are all independent picks, so the probability of ALL of them happening is found by multiplying
the individual probabilities togehher
167/462 x (166/461) x (165/460) x (164/459) x (163/458) x(162/457)x(161/456)
Joe
167 / 462 = 0.361471861 0.07431%
166 / 461 = 0.360086768
165 / 460 = 0.358695652
164 / 459 = 0.357298475
163 / 458 = 0.355895197
162 / 457 = 0.354485777
161 / 456 = 0.353070175
Martin F
Number of ways of choosing 7 red balls is 167c7
Number of ways of choosing 7 balls from 462 is 462c7
Probability all are red = 167c7 ÷ 462c7 = 0.000743