Answer to Question #261109 in Statistics and Probability for Rede

Question

The probability that machine P will breakdown is 2/7 and the probability that machine Q will breakdown is 3/11.Find the probability that at least on machine will be working

Answer 1

The probability that machine P will breakdown is $\frac{2}{7}$

The probability that machine P will not breakdown is $\frac{5}{7}$

The probability that machine Q will breakdown is $\frac{3}{11}$

The probability that machine Q will not breakdown is $\frac{8}{11}$

The probability that at least one machine will be working is $PQ'+P'Q+PQ= (\frac{2}{7}*\frac{8}{11})+(\frac{5}{7}*\frac{3}{11})+(\frac{2}{7}*\frac{3}{11})$

$=\frac{16}{77}+\left(\frac{5}{7}\cdot \frac{3}{11}\right)+\left(\frac{2}{7}\cdot \frac{3}{11}\right)\\ =\frac{16}{77}+\frac{15}{77}+\left(\frac{2}{7}\cdot \frac{3}{11}\right)\\ =\frac{16}{77}+\frac{15}{77}+\frac{6}{77}\\ =\frac{37}{77}$