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

Question

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

Answer 1

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