Suppose that you and a friend are playing cards and you decide to make a friendly wager. the bet is that you will draw two cards without replacement from a standard deck. if both cards are clubs, your friend will pay you $531. otherwise, you have to pay your friend $32. how much would you expect to win or lose?

I will expect to win $1.1156 for the bet.

Explanation:

probability 2 cards are clubs (13/52)*(12/51) = (0.25) * (0.2352)= 0.05882

other 1-0.05882= 0.94118

Expected value= $531 * 0.05882 - $32 (0.94118) =  31.2334- 30.1178

Expected value = $ 1,1156. Making this bet 100 times you will make $111.56

d.

thist title points out that you are explaining the nature of the u.s. government. it is the most specific. a representative government consists of a government where decisions are taken according to a voting system. the most essential aspect of a representative government is found in the different structures where voting rights are granted to different groups of people. for example, voting for governor, mayor, president, local police chief etc.

d. i assume the underlined word is "role." reformat if it isn't.

explanation:

role is closest to part because when replacing words, "playing a vital decision," "playing a vital activity," and "playing a vital dollar" don't make logical sense. the only meaningful choice is "playing a vital part."

this fits one of merriam-webster's definitions of role: "a function or part performed especially in a particular operation or process."