Question

a bag contains 20 marbles. the probability of randomly drawing a red marble is $\frac{1}{4}$. after 5 blue marbles are added to the bag, what is the probability of drawing a red marble?

a. $\frac{1}{4}$
b. $\frac{1}{5}$
c. $\frac{4}{25}$
d. $\frac{1}{2}$

Explanation:

Step1: Calculate the number of red marbles

The probability of drawing a red marble from 20 marbles is $\frac{1}{4}$. Let the number of red marbles be $x$. Using the probability formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$, we have $\frac{x}{20}=\frac{1}{4}$, so $x = 20\times\frac{1}{4}=5$.

Step2: Calculate the new - total number of marbles

After adding 5 blue marbles, the new total number of marbles is $20 + 5=25$.

Step3: Calculate the new probability of drawing a red marble

The number of red marbles remains 5, and the total number of marbles is 25. So the new probability $P=\frac{5}{25}=\frac{1}{5}$.

Answer:

B. $\frac{1}{5}$