Question

Suppose you like to keep a jar of change on your desk. currently the jar contains the followingWhat is the probability that you reach in the jar and randomly grab a quarter and then without replacement a nickel express your answer as a fraction or decimal number rounded to four decimal places

Answer 1

Answer:
`Pr(quarter\text{ and then a nickel\rparen= }(225)/(3916)`

Step-by-step 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)

`\begin{gathered} Pr(quarter\text{ and then a nickel\rparen = }(18)/(89)*(25)/(88) \\ \\ Pr(quarter\text{ and then a nickel\rparen= }(9)/(89)*(25)/(44) \\ \\ Pr(quarter\text{ and then a nickel\rparen = }(225)/(3916) \end{gathered}`