Respuesta :
Given:
There is a bag of coins containing $10 in coins.
The types are,
5 loonies ($1 coin),
10 quarters ($0.25),
20 dimes ($0.10) and
The rest are in nickels ($0.05).
Let the number of coins in nickel is x.
So that,
[tex]\begin{gathered} 5(1)+10(0.25)+20(0.10)+x(0.05)=10 \\ 5+2.5+2+0.05x=10 \\ 0.05x=0.5 \\ x=\frac{50}{5} \\ x=10 \end{gathered}[/tex]Therefore, the number of nickel coins is 10.
The total number of coins is 45.
(i) To find the probability that a chosen coin is $1 coin:
So, the answer is
[tex]\begin{gathered} P(A)=\frac{5}{45} \\ =\frac{1}{9} \end{gathered}[/tex](ii) To find the probability that a chosen coin is $0.10 or $0.05 coin:
So, the answer is,
[tex]\begin{gathered} P(B)=\frac{20}{45}+\frac{10}{45} \\ =\frac{30}{45} \\ =\frac{2}{3} \end{gathered}[/tex](iii) To find the probability that both the two chosen coin dimes coin( with replacement):
So, the answer is,
[tex]\begin{gathered} P(C)=\frac{20}{45}\times\frac{20}{45} \\ =\frac{16}{81} \end{gathered}[/tex](iv) To find the probability that the first coin is a dollar ($1) and the second is a quarter ($0.25): (without replacement)
So, the answer is,
[tex]\begin{gathered} P(D)=\frac{5}{45}\times\frac{10}{44} \\ =\frac{5}{198} \end{gathered}[/tex](v) To find the probability of drawing 2 coins that have a value of exactly $1.25:
So, the value is,
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