# If the chance of picking a red ball is 5%, what's the chances if 3 balls are picked, are they all red?

The ball is not replaced from where it is picked from. There is always a $5\%$ chance you will pick a red ball.

Is it $0.05\times0.05\times0.05$?

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Yes. It's a funny selection of balls you have though, such that not replacing one doesn't change the probabilities. – SiliconCelery Aug 12 '12 at 16:59
@SiliconCelery: It's an infinite ball heat bath :-) – joriki Aug 12 '12 at 17:00
haha yes it is funny... I have used different percentages and a different item from the real question. I don't know if I'm allowed to ask questions on here or not... so thought it safest to change the data. The real data is much more realistic. – Sandra Aug 12 '12 at 17:01
Also specify in advance that the three choices are independent. – GEdgar Aug 12 '12 at 17:02
Ah ok. No problem. Probability is not my strong point. Thank you all for your help. – Sandra Aug 12 '12 at 17:04

To be serious for a second, drawing balls without replacement are naturally going to be considered independent draws. If you start with 5% red balls and draw a red then since you do not repace you have less than 5% red balls for the second draw. Also if you do not pick red you then have more than 5% red balls to select from. An exact answer cannot be given without knowing N the total number of balls to draw from. If N is very large the probability will be less than but close to (0.05)$^3$.

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