Exponential Random Variables QUESTION:
Let $X$ and $Y$ be exponentially distributed random variables with parameters $a$ and $b$ respectively. Calculate the following probabilities:
(a) $P(X&gt;a)$ 
(b) $P(X&gt;Y)$
(c) $P(X&gt;Y+1)$
ANSWER:
(a) since $X$ is exponentially distributed, we have $P(X&gt;a) = 1 - P(X \leq a) = 1 - (1 - e^{-a^2}) = e^{-a^2}$ .
(b) Not sure
(c) Not sure

Any hints/answers would help!!
ad a): As noted by others,$P(X&gt;a)=1-P(X\leq a)$, if you have troubles with this use the expected value of the indicator functions on sets like $\{X&gt;a\}$.

ad b) and c): The link below discusses the same problem. pdf of the difference of two exponentially distributed random variables
$$
\mathbb P(X&gt;Y)
=
\frac b{a+b}ae^{-ax}
$$