Statistics question about percents

Question

5,0.01007431010247],[-2.6,0.012724181705357],[-2.5375,0.015948481633483],[-2.45,0.01983735456099],[-2.3625,0.024A manufacturing machine has a 10% defect rate.

If 6 items are chosen at random, what is the probability that at least one will have a defect?

  

486296371885],[-2.275,0.029994206738768],[-2.1875,0.036460833487169],[-2.1,0.043983596355567],[-2.0125,0.052653811509711],[-1.925,0.062552378033174],[-1.8375,0.073745031931229],[-1.75,0.086277319562377],[-1.6625,0.10016948780033],[-1.575,0.1154115290627],[-1.4875,0.13195865176446],[-1.4,0.14972746691278],[-1.3125,0.16859318595606],[-1.225,0.1883881108589],[-1.1375,0.20890166300605],[-1.05,0.22988214264492],[-0.9625,0.25104033647462],[-0.875,0.27205500069892],[-0.7875,0.2925801450485],[-0.7,0.31225393603],[-0.6125,0.33070893210235],[-0.525,0.34758326725691],[-0.437

Answer 1

use binomial formula: p = probability of a defect = 0.1 n = number of trials = 6 x = number of defects

P(x defects out of n trials) = n! p^x (1-p)^(n-x)

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x!(n-x)!

P(x >= 1) = 1 - P(x = 0)

apply formula for x = 0

6! (0.1)^0 (0.9)^6 = 0.53

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0!6!

P(x >=1 ) = 1 - 0..53 = 0.47