with detailed solution typewritten

1. Diseases A, B and C are prevalent among people in a certain population. It is assumed that 10% of the population will contract disease A sometime during their lifetime, 25% will contract disease B eventually and 20% will contract disease C. 5% will contract diseases A and B, 5% will contract diseases A and C; and, 5% will contract diseases B and C. While 3% will contract all 3 diseases. Find the probability that a randomly chosen person from this population will contract a) at least one disease b) none of the diseases c) at most one disease d) diseases A and B e ) exactly 2 of the diseases