Consider a grating composed of four very narrow slits each separated by a distance \(d\).

(a) What is the probability that a photon strikes a detector centered at the central maximum if the probability that a photon is counted by this detector with a single slit open is \(r\) ?

(b) What is the probability that a photon is counted at the first minimum of this four-slit grating if the bottom two slits are closed? (From Quantum Physics by John S. Townsend.)