Question

Suppose you like to keep a jar of change on your desk currently at the jar contains the followingWhat is the probability that you reach into the jar and grab a penny and then without replacement a dime? Express your answer as a fraction or decimal number rounded to four decimal places

Answer 1

Answer:

The probability of a penny and then without replacement a dime = 7/376

Explanation:

Given:

A jar contains:

6 Pennies, 7 Dimes, 16 Nickels, and 19 Quarters

To find:

the probability when you reach into the jar and grab a penny and then without replacement a dime

Total coins = 6 + 7 + 16 + 19

Total coins = 48

Probability of picking a penny = number of pennies/total coins

Probability of picking a penny = 6/48

Probability of picking a dime after a penny without replacement:

Since we are not replacing the first pick, the total coins will reduce by 1

Total coin for 2nd pick = 48 - 1 = 47

Pr(dime after a penny without replacement) = number of dime/total coin

Pr(dime after a penny without replacement) = 7/47

The probability of a penny and then without replacement a dime = Probability of picking a penny ×

Pr(dime after a penny without replacement)

$\begin{gathered} Pr(penny,\text{ then a dime without replacement\rparen= }\frac{6}{48}\times\frac{7}{47} \\ \\ Pr(penny,\text{ then a dime without replacement\rparen= }\frac{1}{8}\times\frac{7}{47} \\ \\ Pr(penny,\text{ then a dime without replacement\rparen= }\frac{7}{376\frac{}{}} \\ \\ Pr(penny,\text{ then a dime without replacement\rparen= 0.0186} \end{gathered}$