Question

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following. What is the probability that you reach into the jar and randomly grab a nickel and then, without replacement, a dime? Express your answer as a fraction or a decimal number rounded to four decimal places

Answer 1

Answer:

Pr(nickel and dime) = 0.0533

Explanation:

Given:

A jar of change containing 18 pennies, 18 dimes, 16 nickels, 22 quarters

To find:

the probability that you reach into the jar and randomly grab a nickel and then, without replacement, a dime

First, we need to find the probability if the first pick which is a nickel

Pr(nickel) = number nickels/total change

number of nickels = 16

Total change = 18 + 18 + 16 + 22 = 74 coins

$Pr(nickel)\text{ = }\frac{16}{74}$

Next, the probability of picking a dime as the second without replacing the first

Since the first was not replaced, the total number of coins in the jar will reduce by 1 = 74 - 1

Total coins remaining = 73

Pr(picking dime as 2nd coin) = number of dimes/total coins remaining

$Pr(picking\text{ dime as 2nd coin\rparen = }\frac{18}{73}$

Probability (picking nickel and then dime without replacement):

$\begin{gathered} Pr(nickel\text{ and }dime)\text{ = }\frac{16}{74}\times\frac{18}{73} \\ Pr(nickel\text{ and dime\rparen = }\frac{8}{37}\times\frac{18}{73} \\ \\ Pr(nickel\text{ and dime\rparen = 0.0533} \end{gathered}$