JEE Mathematics 2024 Question with Solution

Given: A box contains $10$ red, $30$ white, $20$ blue, and $15$ orange marbles. Two marbles are drawn with replacement.

Find: The probability that the first marble is red and the second marble is white.

First, calculate the total number of marbles:

The probability of drawing a red marble first is:

Since replacement is made, the total number of marbles remains $75$ for the second draw. So the probability of drawing a white marble second is:

These two events are independent, so multiply their probabilities:

Therefore, the probability that the first drawn marble is red and the second drawn marble is white is $\frac{4}{75}$. The correct option is D.

Given: The numbers of marbles are $10$, $30$, $20$, and $15$ for red, white, blue, and orange respectively, and replacement is made after the first draw.

Find: The probability of getting red first and white second.

Using the direct multiplication approach:

Probability of red on the first draw:

Probability of white on the second draw:

Therefore,

Hence, the required probability is $\frac{4}{75}$ and the correct option is D.