Question

1-91 marissa is drawing coins from a bag that contains 5 pennies, 4 nickels, 5 dimes, and 2 quarters.
a) what is the probability that she will draw a nickel? write your answer as a fraction, as a decimal, and as a percent.
b) if one penny, two dimes, and one quarter are added to the bag, what is the new probability that marissa will draw a nickel? write your answer as a fraction, as a decimal, and as a percent.
c) in which situation is it more likely that marissa will draw a nickel?

Explanation:

Part (a)

Step 1: Find total number of coins

First, we calculate the total number of coins in the bag initially. The number of pennies is 5, nickels is 4, dimes is 5, and quarters is 2. So total coins \( n = 5 + 4 + 5 + 2 \).
\( n = 16 \)

Step 2: Calculate probability of nickel

The probability of an event is the number of favorable outcomes (number of nickels) divided by the total number of outcomes (total number of coins). The number of nickels \( f = 4 \). So probability \( P=\frac{f}{n}=\frac{4}{16} \). Simplify the fraction: \( \frac{4}{16}=\frac{1}{4} \).

Step 3: Convert to decimal and percent

To convert the fraction to a decimal, divide 1 by 4: \( \frac{1}{4}= 0.25 \). To convert to a percent, multiply the decimal by 100: \( 0.25\times100 = 25\% \).

Step 1: Find new total number of coins

We add 1 penny, 2 dimes, and 1 quarter to the original bag. Original total was 16. So new total \( n_{new}=16 + 1+ 2 + 1 \).
\( n_{new}=20 \)
The number of nickels remains the same, \( f = 4 \).

Step 2: Calculate new probability of nickel

Probability \( P_{new}=\frac{f}{n_{new}}=\frac{4}{20} \). Simplify the fraction: \( \frac{4}{20}=\frac{1}{5} \).

Step 3: Convert to decimal and percent

To convert the fraction to a decimal, divide 1 by 5: \( \frac{1}{5}=0.2 \). To convert to a percent, multiply the decimal by 100: \( 0.2\times100 = 20\% \).

We compare the probabilities from part (a) and part (b). The probability in part (a) is \( 25\% \) (or \( 0.25 \) or \( \frac{1}{4} \)) and in part (b) is \( 20\% \) (or \( 0.2 \) or \( \frac{1}{5} \)). Since \( 25\%>20\% \), the situation in part (a) (before adding the coins) has a higher probability of drawing a nickel.

Answer:

(a):
Fraction: \( \frac{1}{4} \), Decimal: \( 0.25 \), Percent: \( 25\% \)

Part (b)