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:

Step1: Calculate total number of coins initially

Total number of coins initially = 5 (pennies)+4 (nickels)+5 (dimes)+2 (quarters)=16 coins.

Step2: Calculate probability of drawing a nickel initially

Probability $P_1=\frac{\text{Number of nickels}}{\text{Total number of coins}}=\frac{4}{16}=\frac{1}{4}= 0.25 = 25\%$

Step3: Calculate total number of coins after addition

One penny, two dimes and one quarter are added. New total number of coins = 16+1 + 2+1=20 coins.

Step4: Calculate probability of drawing a nickel after addition

Number of nickels remains 4. New probability $P_2=\frac{4}{20}=\frac{1}{5}=0.2 = 20\%$

Step5: Compare the probabilities

Since $0.25>0.2$, it is more likely to draw a nickel in the first - situation.

Answer:

a. $\frac{1}{4}$, 0.25, 25%
b. $\frac{1}{5}$, 0.2, 20%
c. In the first situation (a) it is more likely that Marissa will draw a nickel.