7. The Monkey at the
Typewriter Suppose that a monkey is seated at a computer
keyboard and randomly strikes the 26 letter keys and the space bar.
Find the probability that its first 24 characters (including
spaces) will be "beware the ides of march". (Leave your answer as a
formula.)
8. The Sorry State Lottery requires you to
select five different numbers from 0 through 56.
(Order is not important.) You are a Big Winner if
the five numbers you select agree with those in the
drawing, and you are a Small-Fry Winner if four of
your five numbers agree with those in the drawing. (Enter
your answers as exact answers.)
What is the probability of being a Big Winner? What
is the probability of being a Small-Fry Winner? What is the
probability that you are either a Big Winner or a Small-Fry
Winner?
9. Lotteries In a
New York State daily lottery game, a sequence
of two digits (not necessarily different) in the range
0-9 are selected at random. Find the probability
that both are different.
10. Poker: Calculate the probability
of being dealt the following poker hand. (Recall that a poker
player is dealt 5 cards at random from a standard deck of 52.)
Express your answer as a decimal rounded to four decimal
places.