Download Example1(1)

Statistical Probability exercises
By
Dr .waleed a.a.
Information technology department
Second stage
Example(1) write down the sample space for the following random
experiments
a)
b)
c)
d)
e)
f)
tossing three coins one time
tossing one coin three time
rolling one 6-sided die (2) time
rolling two 6-sided dice one time
rolling one 4-sided die (2) time
rolling two 4-sided dice one time
Example(2) if you have the following events
A={1,3,5,7,9}
B={2,4,6,8,10}
C={5,10,15,20,25}
write down
1)A ∩B
2) B∩C
3)AU(BC)
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Example(3) (10) different language books,(5) different mathematical
books,(4) different physical are on a shelf. In how many different
ways could you arrange them?
Example(4)if you have the following numbers (3,7,8,9,2)
a)How many odd numbers can you formed from them
b) How many even numbers can you formed from them
c) How many even numbers starting with (7) can you formed from them
d) How many numbers can you formed from them starting with (4)
e) How many numbers can you formed from them starting with (9) and
ending with (2)
f) How many numbers can you formed from them starting with (9) or
with (2)
g) How many numbers can you formed from them starting with (9) or
with (2)
h) How many numbers can you formed from them starting with (9) and
(2)
Example(5). if you have the following numbers (0,1,2,3,4,7)
a)How many odd numbers can you formed from them
b) How many even numbers can you formed from them
c) How many even numbers starting with (7) can you formed from them
d) How many numbers can you formed from them starting with (4)
Example(6) find the number of permutations for the word(depended)
Example(7)We want to paint three rooms in a house, each a different
color, and we may choose from seven different colors of paint. How
many color combinations are possible for the three rooms?
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Example(8). If (20) boys go out for the football team with(12) boys in
each time , how many different teams may be formed?
Example(9)In how many ways can eight people be arranged in a row?
Example(10) Using the digits 4, 5, 6, and 7, how many two-digit
numbers can be formed
a. without repetition?
b. with repetition?
Example(11). Using the digits 4, 5, 6, 7, 8, and 9, how many five-digit
numbers can be formed
a )without repetition?
b) with repetition?
c) how many four-digit odd numbers can be formed without
repetition?
Example(12) From six men and five women, find the number of groups
of four that can be formed consisting of two men and two women.
Example(13) How many different ways can 4 red, 3 blue, 4 yellow, and
2 green bulbs be arranged on a string of Christmas tree lights with 13
sockets?
Example(14)Find the number of possible arrangements of the letters in
the following words:
a) WRITE
b) STRUCTURE
c) HERE
d) MILLIAMPERE
e) TENNESSEE
Example(15)What is the probability of drawing a black marble from a
box of marbles if all 6 of the marbles in the box are white?
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Example(16)What is the probability of drawing a black marble from a
box of 6 black marbles?
Example(17). What is the probability of rolling a pair of dice and
obtaining a total score of 10 or more?
Example(18). A box contains three black pieces of cloth, two striped
pieces, and four dotted pieces. piece is selected randomly and then
placed back in the box. A second piece is selected randomly. What is the
probability that:
(a) both pieces are dotted?
(b) the first piece is black and
the second piece is dotted?
(c) one piece is black and one piece
is striped?
Example(19). A card is drawn at random from a deck. What is the
probability that it is an ace or a king?
Example(20). A card is drawn at random from a deck. What is the
probability it is either a red card or ace
Example(21). Two cards are drawn from a deck (without replacement).
What is the probability they are both diamonds?
Example(22) . The table below lists the results of a student survey
pertaining to favorite ethnic foods. Each student chose only one type of
ethnic food for the survey.
Type
Italian Chinese Japanese Thai Mexican Other
Number
15
20
3
4
30
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Using the given table find the probability that a) a student’s favorite
ethnic food is Chinese, and b) a student’s favorite ethnic food is Mexican.
Example(23): A pair of fair dice is tossed. Determine the probability
that
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a) at least one of the dice shows a 6
b) the sum of the two numbers is 5.
Example(24): From a group of 10 women and 5 men, 2 people are
selected at random to form a committee. Find the probability that
a) Only men are selected
b) Exactly 1 man and 1 woman is selected.
Example(25) One student’s name will be picked at random to win a CD
player. There are 12 male seniors, 15 female seniors, 10 male juniors, 5
female juniors, 2 male sophomores, 4 female sophomores, 11 male
freshmen and 12 female freshman. Find the probability that
a) a senior or a junior is picked
b) a freshman or a female is picked
c) a freshman is NOT picked.
Example(26): If two cards are drawn from a deck of cards, WITH
REPLACEMENT, find the probability that the 1st card is a heart AND
the 2nd card is an ace.
Example(27). Consider the random experiment of rolling a fair die and
flipping a fair coin.
a) Write down the sample space
b) Find the probability of getting the number (3) on the die
c) Find the probability that the coin lands on heads
d) The probability that the number on the die is less than (3)
Example(28).Consider the random experiment of rolling three fair dice
one time
a) find the sample space
b) the probability that all number on the three dice are equal
c) the probability that the number on the 1st die (2 or 1) ,2nd die (odd
number ),3rd die (even number)
Example(29) two urns the 1st contain (3) black (2) white balls ,2nd
contain (4) black (6) white balls
One urn is drawing and select one ball at random find
a) what is the probability that the selected ball is black
b) what is the probability that the selected ball is white
Example(30) a box contains (5)red and (4) white marbles . two marbles
are drawn successively from the box without replacement and it is noted
that the second one is white .what is the probability that the first is also
white?
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http://www.isye.gatech.edu/~rserfozo/courses/isye2027/NotesChapters1--3.pdf.
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