QJEEM24Ma964c: JEE Main 2024 Mathematics - Class 12 JEEM24Ma964c Solution: Two marbles are drawn in succession from a box containing 10…

To solve this problem, we need to calculate the probability of two independent events occurring in succession: the first marble drawn is red, and the second marble drawn is white. Since the drawing is with replacement, the number of marbles of each color remains the same for both draws.

The total number of marbles in the box is the sum of red, white, blue, and orange marbles:

The probability of drawing a red marble in the first draw is the number of red marbles divided by the total number of marbles:

Since the marble is replaced, the probability of drawing a white marble in the second draw remains as the number of white marbles divided by the total number of marbles:

The probability of both independent events occurring in succession (drawing a red marble first and then a white marble) is the product of their individual probabilities:

Now, let's calculate this probability:

$P(\text{First is red and second is white}) = \frac{10 \times 30}{75 \times 75} = \frac{300}{5625}= \frac{4}{75}.$

Therefore, the correct answer is