Question

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

Answer 1

Answer:

$P(Nickel\ and\ Nickel) = 0.08091$

Step-by-step explanation:

Given

$Pennies = 18$

$Dimes = 13$

$Nickels = 18$

$Quarters = 13$

Required

Probability of selecting 2 nickels without replacement

This can be represented as: $P(Nickel\ and\ Nickel)$

The solution is as follows

$P(Nickel\ and\ Nickel) = \frac{Nickel}{Total}*\frac{Nickel-1}{Total-1}$

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:

$P(Nickel\ and\ Nickel) = \frac{18}{62}*\frac{18-1}{62-1}$

$P(Nickel\ and\ Nickel) = \frac{18}{62}*\frac{17}{61}$

$P(Nickel\ and\ Nickel) = \frac{18*17}{62*61}$

$P(Nickel\ and\ Nickel) = \frac{306}{3782}$

$P(Nickel\ and\ Nickel) = 0.08091$