I have the following question as practice for an upcoming test:
A website suggests that men think about sex an average of $15$ times per day.
Let $x$= the number of hours that pass between successive thoughts of sex, = $1.6$
At least $1.6$ hours have passed since the last thought of sex. What is the probability that in total, at least $3.2$ hours will pass until the next thought of sex?
I thought since Exponential Distributions are memoryless, that this would just be $P(x \ge 3.2)$, but apparently this is wrong.
You're right that the exponential distribution is memoryless. That is,
$$P(X\geq 3.2 \mid X \geq 1.6)=P(X\geq1.6)$$
Perhaps the wording of the question threw you off.
It's looking for the probability that you have to wait at least $3.2$ hours in total so $1.6$ more hours.
which of course comes out to be
$$\begin{align*} P(X\geq1.6) &=1-P(X\lt1.6)\\\\ &=1-\int_0^{1.6} \frac{1}{1.6}e^{-\frac{x}{1.6}}dx\\\\ &\approx 0.36788 \end{align*}$$