Suppose we have an urn with 2 balls, one red and one white. The probability to get a white one is P(B) = p. Suppose we repeat the experiment k times in order to get the white ball for the first time. X is the number of tries.
if p = 3/4, find P(3≤X<6)
Probability question?
2018-10-15 11:24 pm
回答 (1)
2018-10-15 11:33 pm
X = 1: Chance of getting white the first time: 3/4
X = 2: Chance of getting red, then white: (1/4) * (3/4) = 3/16
X = 3: Chance of getting two red, then white: (1/4)^2 * (3/4) = 3/64
X = 4: Chance of getting three red, then white: (1/4)^3 * (3/4) = 3/256
X = 5: Chance of getting four red, then white: (1/4)^4 * (3/4) = 3/1024
Chance of X = 3, 4, or 5:
(3/64) + (3/256) + (3/1024) = 63/1024 = 0.0615234375 = 6.15234375%
X = 2: Chance of getting red, then white: (1/4) * (3/4) = 3/16
X = 3: Chance of getting two red, then white: (1/4)^2 * (3/4) = 3/64
X = 4: Chance of getting three red, then white: (1/4)^3 * (3/4) = 3/256
X = 5: Chance of getting four red, then white: (1/4)^4 * (3/4) = 3/1024
Chance of X = 3, 4, or 5:
(3/64) + (3/256) + (3/1024) = 63/1024 = 0.0615234375 = 6.15234375%
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