Probability question (quick, I hope)?

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%.

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)

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

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