We are going to obtain binomial probabilities associated with n = 22 trials when

Question

We are going to obtain binomial probabilities associated with n = 22 trials when the probability of a success in any given trial is = 0.1.

Suppose the probability of a bike getting stolen in Honolulu is 10% and 22 bikes are randomly selected in Honolulu.

1) What is the probability that 3 of them will be stolen?

2) What is the probability that at least 5 of them will be stolen?

use the probabilities below:

x P(x=k) P(x<=k) 0 0.098477 0.098477 1 0.240722 0.339199 2 0.280842 0.620041 3 0.208031 0.828072 4 0.109794 0.937866 5 0.043918 0.981784 6 0.013826 0.99561 7 0.003511 0.999121 8 0.000732 0.999853 9 0.000126 0.999979 10 1.83E-05 0.999998 11 2.21E-06 1 12 2.25E-07 1 13 1.93E-08 1 14 1.38E-09 1 15 8.16E-11 1 16 3.97E-12 1 17 1.55E-13 1 18 4.8E-15 1 19 1.12E-16 1 20 1.87E-18 1 21 1.98E-20 1 22 1E-22 1

Explanation / Answer

1) The probability that 3 of the bikes will be stolen is given by P[X=3] =0.208031

2) The probability that at least 5 of the bikes will be stolen is given by P[X>=5]=1-P[X<5] = 1-0.981784 = 0.018216

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