What does the idiom "Keep one's fingers crossed" mean?

Global strategies to control infective disease have historically included the erection of barriers to international travel and __ (24)- Keeping people with such deadly disease outside national borders has - (25)- as an important public health policy in the human immunodeficiency virus (HIV) epidemic. Between 29 and 50 countries - (26) - to have introduced border restrictions on HIV-positive foreigners, usually those planning an- (27)- stay in the country, such as students, workers or seamen.

A group of eight people is made up of three teams. Team-I consists of two women M and N, Team-II consists of three men O, P and Q and Team-III consists of three children R, S and T. Each of the people must be on one and only one of three categories formed according to the following conditions. Each category must have either two or three members Each team must have at least one child M and R cannot be on the same team P and Q cannot be on the same team O and S must be on the same team If two men are on a team together, who of the following must be on a team with only one other member?