The gamma tail carries a 1 plus x over 2 factor the exponential does not

A mobile manufacturing company uses two brands of batteries for its mobiles. The life (in years) of batteries of Brand I follows an exponential distribution with the probability density function f(x) = $e^{-x}$ if x > 0 and 0 otherwise, and that of Brand II follows a gamma distribution with the probability density function g(x) = $(x/4)e^{-x/2}$ if x > 0 and 0 otherwise. The company uses the batteries of Brands I and II in proportion of 20% and 80% respectively, in its mobiles. The probability that a randomly selected mobile has the battery life more that 2 years is