Answer to Question #1737 in Statistics and Probability for Tim

Question

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.

Answer 1

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.