511 Counting
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Transcript of 511 Counting
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7/25/2019 511 Counting
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STAT 511 Counting Handout
1. The population of a town is 20,000. If each resident has three initials, is it truethat at least two people have the sae initials! "#plain.
2. $o% has nine guests to his house, two of which are &ane and 'ind(. If the guests
arrive in rando order, what is the pro%a%ilit( that)
&ane will not arrive right after 'ind(!
&ane arrives %efore 'ind( and at least * people arrive %etween the!
+. ne of the elevators in the 'ath %uilding starts with * people and stops at -floors. Assuing it is euall( li/el( that a passenger gets off at an( of these -
floors, what is the pro%a%ilit( that)
no%od( gets off on the thor -thfloor!
at least two passengers get off on the sae floor!
. In how an( different wa(s can 1* offices %e painted if)
each office is paint with one of four different colors!
each of four different colors is used e#actl( ties!
5. ive different nu%ers are chosen at rando fro 0 to 33. 4hat is thepro%a%ilit( that)
all five nu%ers selected are odd!
the nu%er - is chosen!
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ptional)
*. How an( eight digit nu%ers are there without two identical nu%ers ne#t toeach other!
. A ultiple choice test has 20 uestions, each having five possi%le answers. "ach
uestion has onl( one correct answer. If the uestions are answered at rando,what is the pro%a%ilit( of getting)
all of the right!
at least 1- right!
-. Suppose 1 arried couples ta/e part in a contest. ourteen identical pries are
given to 1 different individuals, with each person having an eual chance of
winning one of the pries. 4hat is the pro%a%ilit( that)
one person in each couple wins a prie!
e#actl( couples win all 1 pries!
3. In a closet there are - pairs of shoes. Si# shoes are selected at rando. 4hat isthe pro%a%ilit( of getting)
no atching pairs!
onl( one pair of atching shoes!
two pairs of atching shoes!
three pairs of atching shoes!