Question

In a box full of red and green color marbles, there are $20$ red and $30$ green marbles. What is the theoretical probabilty that a blind-folded person draws a red marble on the first attempt?

• A. $30$ out of $50$, which is $\frac{30}{50}$ or $\frac{3}{5}$
  
• B. $20$ out of $50$, which is $\frac{20}{50}$ or $\frac{2}{5}$
  
• C. $20$ out of $30$, which is $\frac{20}{30}$ or $\frac{2}{3}$
  
• D. $50$ out of $50$, which is $\frac{50}{50}$ or $\frac{5}{5}$
  

Answer 1

The correct option is B $20$ out of $50$, which is $\frac{20}{50}$ or $\frac{2}{5}$


Given:
Number of red marbles $=20$
Number of green marbles $=30$

$\text{Total number of marbles available in the box}$ $=$ $\text{Number of red marbles}$ $+$ $\text{Number of green marbles}$

$=20+30$
$=50$

Let $\text{P(R)}$ denotes the theoretical probability that a blind-folded person draws a red marble on the first attempt.

$\text{P(R)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$


In this situation,

Number of favorable outcomes $=20$ ($\because$ There are $20$ red marbles in the box)

Total number of outcomes $=50$ ($\because$ There are $50$ total marbles in the box)

$\text{P(R)}=\frac{20}{50}$
$\text{P(R)}=\frac{2}{5}$

The theoretical probability that a blind-folded person draws a red marble on the first attempt is $\frac{20}{50}$ or $\frac{2}{5}$.

Therefore, option (b.) is the correct answer.