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A very large bag contains more coins than you are willing to count. Instead, you draw a random sample of coins from the bag and record the following numbers of each type of coin in the sample before returning the sampled coins to the bag. If you randomly draw a single coin out of the bag, what is the probability that you will obtain either a quarter or a penny

Respuesta :

MrRoyal

Missing Details

Quarters  ≡ Dimes ≡  Nickels ≡  Pennies

23             ≡   29      ≡  17           ≡  38

Answer:

[tex]P(Q\ or\ P) = 0.5701[/tex]

Step-by-step explanation:

Given

[tex]Quarters = 23[/tex]

[tex]Dimes = 29[/tex]

[tex]Nickels = 17[/tex]

[tex]Pennies = 38[/tex]

First, we calculate total number of coins

[tex]Total = 23 + 29 + 17 + 38[/tex]

[tex]Total = 107[/tex]

The probability of obtaining quarter (Q) of penny (P) is:

[tex]P(Q\ or\ P) = P(Quarters) + P(Pennies)[/tex]

[tex]P(Q\ or\ P) = \frac{n(Quarters)}{Total} + \frac{n(Pennies)}{Total}[/tex]

Take LCM

[tex]P(Q\ or\ P) = \frac{n(Quarters) + n(Pennies)}{Total}[/tex]

[tex]P(Q\ or\ P) = \frac{23 + 38}{107}[/tex]

[tex]P(Q\ or\ P) = \frac{61}{107}[/tex]

[tex]P(Q\ or\ P) = 0.5701[/tex]