The probability that none of the devices fails happens when x = 0.
P(none fail) = 1(0.01)^(0)•(1 - 0.01)^(10)
P(none fail) = (0.01)^0•(0.99)^(10)
P(none fail) = 0.90438
Answer:
Probability that none of your devices fail is 0.9044.
Step-by-step explanation:
We are given that the Environmental Protection Agency (EPA) has contracted with your company for equipment to monitor water quality for several lakes in your water district. A total of 10 devices will be used. Assume that each device has a probability of 0.01 of failure during the course of the monitoring period.
The above situation can be represented through Binomial distribution;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 10 devices
r = number of success = none fail
p = probability of success which is probability of failure during the
course of the monitoring period, i.e; 0.01.
LET X = No. of failures
So, it means X ~ [tex]Binom(n=10, p=0.01)[/tex]
Now, Probability that none of your devices fail is given by = P(X = 0)
P(X = 0) = [tex]\binom{10}{0} \times 0.01^{0} \times (1-0.01)^{10-0}[/tex]
= [tex]1 \times 1 \times 0.99^{10}[/tex] = 0.9044
Hence, the probability that none of your devices fail is 0.9044.
