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)
[tex]\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}[/tex]