Question

A DELL computer hardware has a yearly 17% rate of failure. Answer the following question. Convert your answer to a percentage. What is the probability that if you buy four computers, at least 1 will fail within a year?

Answer 1

Let X be num of computers that will not fail. P(X >= 1) = 1 - P(X = 0) P(X=0) is probability that ALL 4 computers fail P(X>=1) = 1 - (.17)^4 = 0.99916 = 99.916%

Answer 2

Failure of a Single Dell computer in terms of percentage=17%

It means you buy a computer, there is 17% chance that it will be bad Machine and (100-17)%=83% chance that, it will be a good machine.

Probability that if you buy four computers, atleast 1 will fail within a year

`=_(1)^(4)\textrm{P}* [P(S)]^3* P(F)+_(2)^(4)\textrm{P}* [P(S)]^2* [P(F)]^2+_(3)^(4)\textrm{P}* P(S)* [P(F)]^3+_(4)^(4)\textrm{P}* [P(F)]^4\\\\=4 * (0.83)^3* (0.17)+6* (0.83)^2* (0.17)^2+4* (0.83)* (0.17)^3+1* (0.17)^4\\\\=0.3881516+0.11945526+0.01631116+0.00083521\\\\=0.52475323`

=0.53(Approx)

=0.53 × 100

=53%