In each month, the proportion of "Prize" bonds that win a prize is 1 in 11000. There is a large number of prizes and all bonds are equally likely to win each prize. Show that, for a given month, the probability that a bondholder with 5000 bonds wins at least one prize is 0.365.

For a given month find:

1) The probability taht in a group of 10 bondholders each holding 5000 bonds, four or more win at least one prize,

2) The probability in a group of 100 bondholders each holding 5000 bonds, 40 or more win at least one prize.
Find the expected number of prizes for a bondholder holding 550 bonds for 24 months.