The random variable T represents the lifetime in years of a component of a solar cell. Its probability density function is F(t)=0.4 e^{-0.4 t}, quad t geqslant 0.
a. Find the probability that this component of the solar cell fails within 1 year.
b. Each solar cell has 5 of these components which operate independently of each other. The cell will work provided at least 3 of the components continue to work. Find the probability that a solar cell will still operate after 1 year.
a) 0.32968 and 0.26368
b) 0.67032 and 0.73632
c) 0.32968 and 0.73632
d) 0.26368 and 0.67032