Question

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 22 Pennies 27 Dimes 9 Nickels 30 Quarters What is the probability that you reach into the jar and randomly grab a penny and then, without replacement, a dime

Answer 1

Answer:

$P(Penny\ and\ Dime) = \frac{9}{116}$

Step-by-step explanation:

Given

$Pennies = 22$

$Dimes = 27$

$Nickels = 9$

$Quarters = 30$

Required

$P(Penny\ and\ Dime)$

This is calculated as:

$P(Penny\ and\ Dime) = P(Penny) * P(Dime)$

Since it is a selection without replacement, the computation is:

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

So, we have:

$P(Penny\ and\ Dime) = \frac{22}{22+27+9+30} * \frac{Dime}{22+27+9+30-1}$

$P(Penny\ and\ Dime) = \frac{22}{88} * \frac{27}{87}$

$P(Penny\ and\ Dime) = \frac{1}{4} * \frac{9}{29}$

$P(Penny\ and\ Dime) = \frac{9}{116}$