Answer to Question #1737 in Statistics and Probability for Tim

Question #1737
1000 black beans in a a jar, plus 1 green bean. If 999 people draw beans from the jar, what is the probability of each one drawing the green bean? Need the answer and the equation that leads to the answer, please.
Expert's answer
1. 1000 black beans, 1 green bean.
Probability for 1st man men to get black bean
P1 (black) = 1000/1001.
Probability for 1st man men to get green bean
P1 (green) = 1/1001.
2. 999 black beans, 1 green bean(we suppose that beans we don’t put beans back).
Probability for 2nd man men to get black bean
P2 (black) = 999/1000
P2 (green) = P1 * 1/1000 = 1000/1001 * 1/1000

3. 998 black beans ,1 green
P3 (black) = 998/999
P3 (green) = P1 (g)P2 (g) * 1/1000 = 1000/1001 * 999/1000 * 1/999

n. For 999th man probability will be
P999 (green) = P1 (g) P2 (g)…P997 (g) P998 (g) * 1/1000 = 1000/1001 * 999/1000*…*3/4 * 2/3 * 1/2
If after a draw beans go back to jar probability for everyone will be the same and will be equal
P(black) = 1000/1001.
P(green) = 1/1001.

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Assignment Expert
18.11.14, 17:30

Dear doubt.
Thank you for your question. In this experiment the output of a previous trial is very important, because if a person picks out a green bean, then probability, that other person will take out a green bean, equals zero. We use probability of intersection of events and conditional probability: P(C and D)=P(C)*P(D/C), where P(C)=P1, P(D/C)=1/1000.

17.11.14, 20:04

if u don't mind i have a doubt
can i know why is P2 (green) = P1 * 1/1000 and not 1/1000 ??????

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