Probability Question Help (1 Viewer)

[pmtyo]

Hi guys, was just wondering if anyone could help me with part ii) of this question. I have the bold answer, no fully worked solutions:

A number of electrical components are wired together in an alarm so that it will operate if at least one of the components works. The probability that each of these components will work is 0.6

i) If an alarm had 3 components wired together, find the probability that at least one of the components will work. (0.936)

ii) Find the minimum number of components that must be wired together to be 99% certain that the alarm will operate. (n = 5)

I know you use log and all but I don't know where to begin

 

[faisalabdul16]

Hi guys, was just wondering if anyone could help me with part ii) of this question. I have the bold answer, no fully worked solutions:

A number of electrical components are wired together in an alarm so that it will operate if at least one of the components works. The probability that each of these components will work is 0.6

i) If an alarm had 3 components wired together, find the probability that at least one of the components will work. (0.936)

ii) Find the minimum number of components that must be wired together to be 99% certain that the alarm will operate. (n = 5)

I know you use log and all but I don't know where to begin

the way you do ii is by forming an inequality

1-(0.4)^n >0.99
0.01 > (0.4)^n
Take log of both sides
log(0.01) > nlog(0.4)
log(0.01)/log(0.4) > n
n < log(0.01)/log(0.4)
chuck into calculator and you'll get
n < 5.02588....
n has to be a whole number
therefore n = 5

need to learn how to use latex hahah hope you understood this

 

[pmtyo]

Thanks, very helpful!