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

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:

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