Question

Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is

• A. \(\frac{2}{25}\)
• B. \(\frac{4}{25}\)
• C. \(\frac{2}{3}\)
• D. \(\frac{4}{75}\)

Answer 1

The Correct Option is D

To find the probability that the first drawn marble is red and the second drawn marble is white, with replacement after each drawing, we start by understanding the probability formulas involved: 

1.  Calculate the total number of marbles in the box:
   • Red marbles: 10
   • White marbles: 30
   • Blue marbles: 20
   • Orange marbles: 15
2. Find the probability of drawing a red marble first:
   • The number of red marbles = 10
   • Probability of red marble = \(\frac{10}{75}\) = \(\frac{2}{15}\)
3. Since replacement is made, the total number of marbles remains 75 for the second draw:
4. Find the probability of drawing a white marble second:
   • The number of white marbles = 30
   • Probability of white marble = \(\frac{30}{75}\) = \(\frac{2}{5}\)
5. By multiplying the probabilities of the two independent events (since replacement is made, they are independent), we find the overall probability:
   • Probability = Probability (Red first) × Probability (White second)
   • = \(\frac{2}{15} \times \frac{2}{5}\) = \(\frac{4}{75}\)

Therefore, the probability that the first drawn marble is red and the second drawn marble is white is \(\frac{4}{75}\).

The correct answer is: \(\frac{4}{75}\).

Answer 2

The total number of marbles in the box is:

$10 + 30 + 20 + 15 = 75$

The probability of drawing a red marble first is:

$\frac{10}{75}$

Since replacement is made, the probability of drawing a white marble next is:

$\frac{30}{75}$

Therefore, the combined probability of first drawing a red marble and then a white marble is:

$\frac{10}{75} \times \frac{30}{75} = \frac{4}{75}$