Answer: [tex]Pr(quarter\text{ and then a nickel\rparen= }\frac{225}{3916}[/tex]
Explanation:
Given:
Total coins in the jar:
27 Pennies, 19 Dimes, 25 Nickels, and 18 Quarters
To find:
the probability that you reach in the jar and randomly grab a quarter and then without replacement a nickel
Total coins = 27 + 19 + 25 + 18 = 89
To determine the probability of picking a quarter and then a nickel without replacement, we will find the probability of picking a quarter 1st and a nickel second
Pr(nickel) = number of quarter/total
Pr(quarter 1st) = 18/89
Pr(nickel 2nd) = number of nickels/total
The total coins will change for the nickel as the first pick (quarter) was not replaced. This means the total will reduce by 1
89 - 1 = 88
Pr(nickel 2nd) = 25/88
probability of picking a quarter and then a nickel without replacement = Pr(quarter 1st) × Pr(nickel 2nd)
[tex]\begin{gathered} Pr(quarter\text{ and then a nickel\rparen = }\frac{18}{89}\times\frac{25}{88} \\ \\ Pr(quarter\text{ and then a nickel\rparen= }\frac{9}{89}\times\frac{25}{44} \\ \\ Pr(quarter\text{ and then a nickel\rparen = }\frac{225}{3916} \end{gathered}[/tex]
