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When a computer generates random digits, the probability that any particular digit in the set {0, 1, 2, ..., 9} is generated on any individual trial is 1/10 = 0.1. Suppose that we are generating digits one at a time and let X = the number of digits that the computer generates to get the first zero. Determine the probability that the first 0 occurs on the seventh random digit generated.

Respuesta :

Answer:

0.0531

Step-by-step explanation:

This is a typical Geometric Probability question.

Let X = digit 0

then X' = all other 9 digits except 0

P(X) = 0.1

P(X') = 0.9

If 0 (X) first occurs on the 7th event, that means for the 1st to 6th event would be other digits besides 0 (X'). Therefore, the probability:

P = P(1st event) × P(2nd event) × P(3rd event) × P(4th event) × P(5th event) × P(6th event) × P(7th event)

  = P(X') × P(X') × P(X') × P(X') × P(X') × P(X') × P(X)

  = (P(X'))⁶ × P(X)

  = 0.9⁶ × 0.1

  = 0.0531

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