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A wallet contains five $10 bills, three $5 bills, six $1 bills, and no larger denominations. If bills are randomly selected one-by-one from the wallet, what is the probability that at least two bills must be selected to obtain the first $10 bill?

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Answer:

[tex]\frac{4}{21}[/tex]

Step-by-step explanation:

Another way of phrasing this question is this; if only two bills are selected without replacement, what is the probability that at one of the two bills will be a $10 bill:

P(One $10 bill) = P(picking a $10 bill first then another type) + (picking another

                            type then a $10 bill)

                        = [tex]\frac{5}{15}*\frac{10}{14}+\frac{10}{15} *\frac{5}{14} = \frac{4}{21}[/tex]

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