Before Dawn Josh Hurriedly Packed Some Clothes for a Job-Interview

Short Answer

Before dawn Josh hurriedly packed some clothes for a job-interview trip while his roommate was still sleeping. He reached in his disorganized sock drawer where there were five black socks and five navy blue socks, although they appeared to be the same color in the dimly lighted room. Josh grabbed six socks, hoping that at least two, and preferably four, of them were black to match the gray suit he had packed. With no time to spare, he then raced to the airport to catch his plane.
a. What is the probability that Josh packed at least two black socks so that he will be dressed appropriately the day of his interview?
b. What is the probability that Josh packed at least four black socks so that he will be dressed appropriately the latter day of his trip as well?