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Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 18 Pennies13 Dimes 18 Nickels13 Quarters What is the probability that you reach into the jar and randomly grab a nickel and then, without replacement, another nickel

Sagot :

MrRoyal

Answer:

[tex]P(Nickel\ and\ Nickel) = 0.08091[/tex]

Step-by-step explanation:

Given

[tex]Pennies = 18[/tex]

[tex]Dimes = 13[/tex]

[tex]Nickels = 18[/tex]

[tex]Quarters = 13[/tex]

Required

Probability of selecting 2 nickels without replacement

This can be represented as: [tex]P(Nickel\ and\ Nickel)[/tex]

The solution is as follows

[tex]P(Nickel\ and\ Nickel) = \frac{Nickel}{Total}*\frac{Nickel-1}{Total-1}[/tex]

The second nickel is reduced by 1 because the first nickel was not replaced and this also reduces the total by 1

So, we have:

[tex]P(Nickel\ and\ Nickel) = \frac{18}{62}*\frac{18-1}{62-1}[/tex]

[tex]P(Nickel\ and\ Nickel) = \frac{18}{62}*\frac{17}{61}[/tex]

[tex]P(Nickel\ and\ Nickel) = \frac{18*17}{62*61}[/tex]

[tex]P(Nickel\ and\ Nickel) = \frac{306}{3782}[/tex]

[tex]P(Nickel\ and\ Nickel) = 0.08091[/tex]

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