Answer to Question #207873 in Statistics and Probability for key

Question

A flashlight has 8 batteries, 5 of which are defective. If 5 are selected at random without replacement, find the probability that all of them are defective. Enter your answer as a fraction or a decimal rounded to 3 decimal places. The probability of getting all of them defective batteries is 

.

Answer 1

Probability to select defective batterу from 8 batteries 5 of which are defective:

P₁ = 5/8;

After that we have only 7 batteries 4 of which are defective. Probability select defective batterу

equals:

P₂ = 4/7;

After that we have only 6 batteries 3 of which are defective. Probability select defective batterу

equals:

P₃ = 3/6;

After that we have only 5 batteries 2 of which are defective. Probability to select defective batterу

equals:

P₄ = 2/5;

After that we have only 4 batteries 1 of which are defective. Probability to select defective batterу

equals:

P₅ = 1/4;

Finally, total probability equals:

$P=P_1\times P_2\times P_3\times P_4\times P_5=(\frac{5}{8})\times(\frac{4}{7})\times(\frac{3}{6})\times(\frac{2}{5})\times(\frac{1}{4})=\frac{1}{56}=0.0179$