Question 733109: Hello,
If the probability of an event occuring is 10%, what is the probability that 2 or more times the event will occur in 30 , 40 or 50 trials. In the case of 30 trials I have been using the formula P(2 out of 30) = (30! / (2!*(30-2)!) *.01*(0.9*10^28). I get 22.7%. I think that I am calculating exactly 2 events occuring. How do I calculate at least 2 events?
Thanks.
Ross
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If the probability of an event occuring is 10%, what is the probability that 2 or more times the event will occur in 30 , 40 or 50 trials. In the case of 30 trials I have been using the formula P(2 out of 30) = (30! / (2!*(30-2)!) *.01*(0.9*10^28). I get 22.7%. I think that I am calculating exactly 2 events occuring. How do I calculate at least 2 events?
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Binomial Problem with n = 30 and p(event) = 0.1
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P(2<= x <=30) = 1 - [P(x = 0)+P(x=1)]
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= 1 - [30C0(0.1)^0*0.9^30 + 30C1(0.1)^1*(0.9)^29]
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Now using a TI-84 calculator:
= 1 - binomcdf(30,0.1,1) = 0.8163
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Cheers,
Stan H.
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