Answer
a) At $x=1$
b) 1000 photons.
Work Step by Step
$$\color{blue}{\bf [a]}$$
From the given figure, the photon is more likely to be detected at $x=1$ m than at $x=0$ m since the probability density is higher there.
$$\color{blue}{\bf [b]}$$
To find the expected number of photons in the interval at $ x = 0.50 \;\text{m} $, we need to calculate the probability of detecting a photon in this small interval.
From the given graph, the probability density at $ x = 0.50 \;\text{m} $ is $ 1\; \rm{m}^{-1} $.
The interval at $ x = 0.50 \; \text{m} $ is 1 mm wide,
So the expected number of photons in the interval is given by
$$N_{\rm Expected \;photons}= P(x) \delta x \times \text{Total number of photons} $$
Plugging the known;
$$N_{\rm Expected \;photons}=(1)(1\times 10^{-3})(10^6) =\color{red}{\bf 1000}\;\rm photons $$
