Section 7.4 Use of Counting Techniques in Probability
Question: Five marbles are selected at random without replacement from a jar containing four white
marbles and six blue marbles. From Section 6.4, we know that there are
ways to
choose these five marbles. We should also know that
of those samples have all blue
marbles. How do we find the probability that our sample has all blue marbles?
Computing the Probability of an Event in a Uniform Sample Space: Revisited
Let S be a uniform sample space, and let E be any event. Then
P (E) =
Number of outcomes in E
n(E)
=
Number of outcomes in S
n(S)
Let’s revisit the above question:
1. Five marbles are selected at random without replacement from a jar containing four white marbles
and six blue marbles. Find the probability of the given event. (Round answer to three decimal
places.)
All of the marbles are blue.
2. A 4-card hand is drawn from a standard deck of 52 playing cards. Find the probability that the
hand contains the given cards. (Round answer to 3 decimal places.)
No diamonds.
3. Three cards are selected at random without replacement from a well-shu✏ed deck of 52 playing
cards. Find the probability of the given event. (Round answer to four decimal places.)
Three cards of the same suit are drawn.
4. A box has 7 marbles, 3 of which are white and 4 of which are red. A sample of 4 marbles is
selected randomly from the box without replacement. (Give answers as an exact fraction.)
(a) What is the probability that exactly 2 are white and 2 are red?
(b) What is the probability that at least 2 of the marbles are white?
t.si#
5. Jacobs & Johnson, an accounting firm, employs 20 accountants, of whom 6 are CPAs. If a
delegation of 4 accountants is randomly selected from the firm to attend a conference, what is
the probability that 4 CPAs will be selected? (Round answer to three decimal places.)
6. A shelf in the Metro Department Store contains 90 colored ink cartridges for a popular ink-jet
printer. Eight of the cartridges are defective. (Round answers to five decimal places.)
(a) If a customer selects 2 cartridges at random from the shelf, what is the probability that both
are defective?
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Fall 2016,
Maya Johnson
(b) If a customer selects 2 cartridges at random from the shelf, what is the probability that at
least 1 is defective?
7. A customer from Cavallaro’s Fruit Stand picks a sample of 4 oranges at random from a crate
containing 65 oranges, of which 5 are rotten. What is the probability that the sample contains 1
or more rotten oranges? (Round answer to three decimal places.)
8. A student studying for a vocabulary test knows the meanings of 14 words from a list of 26 words.
If the test contains 10 words from the study list, what is the probability that at least 8 of the
words on the test are words that the student knows? (Round answer to three decimal places.)
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Fall 2016,
Maya Johnson