Cumulative distribution function of exponential distribution is given by $F(x) = 1 - e^{-\lambda x}$, where $\lambda$ is the rate of occurrence of event. (

https://en.wikipedia.org/wiki/Exponential_distribution#Cumulative_distribution_function )

So for example, $F(8)$ means component survives at most 8 years.

Here mean time of failure is 5 years i.e. rate parameter $\lambda$ is 1/5 = 0.2.

(a) Probability of component working even after 8 years is $1 - F(8) = 1 - (1-e^{-0.2*8}) = e^{-1.6} \approx 0.20 $

Hence option (4) is correct.

(b) Probability that at least 2 systems are working = 1 - (prob of no system working + prob of 1 system working)

Let probability of a system working after 8 years is $p$, which is 0.20 as calculated earlier.

So required probability is

$$P = 1 - \binom{5}{0}(p)^0(1-p)^5 - \binom{5}{1}(p)^1(1-p)^4 \approx 0.2627$$

Hence option (4) is correct.