# Answer to Question #26038 in Statistics and Probability for k mill

Question #26038

a flashlight has 10 batteries 5 of which are defective if 5 are selected at random without replacement find the probability that all of them are defective

Expert's answer

Probability to select defective batterу from 10 batteries 5of which are defective:

P1 = 5/10 = 1/2

After that we have only9 batteries 4 of which are defective. Probability select defective batterу

equals:

P2 = 4/9

After that we have only8 batteries 3 of which are defective. Probability select defective batterу

equals:

P3 = 3/8

After that we have only7 batteries 2 of which are defective. Probability to select defective batterу

equals:

P4 = 2/7

After that we have only6 batteries 1 of which are defective. Probability to select defective batterу

equals:

P5 = 1/6

Finally, totalprobability equals:

P = P1*P2*P3*P4*P5 =1/2*4/9*3/8*2/7*1/6 = 1/252 ( = 0.00396825)

Answer: probabilitythat all of them are defective equals 1/252

P1 = 5/10 = 1/2

After that we have only9 batteries 4 of which are defective. Probability select defective batterу

equals:

P2 = 4/9

After that we have only8 batteries 3 of which are defective. Probability select defective batterу

equals:

P3 = 3/8

After that we have only7 batteries 2 of which are defective. Probability to select defective batterу

equals:

P4 = 2/7

After that we have only6 batteries 1 of which are defective. Probability to select defective batterу

equals:

P5 = 1/6

Finally, totalprobability equals:

P = P1*P2*P3*P4*P5 =1/2*4/9*3/8*2/7*1/6 = 1/252 ( = 0.00396825)

Answer: probabilitythat all of them are defective equals 1/252

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