A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be (i) white? (ii) blue? (iii) red?

Step 1: Calculate the total number of marbles

To find the total number of possible outcomes, we add the number of marbles of each color present in the box. This sum represents the total number of marbles available to be drawn.

Step 2: Substitute values and compute total

We are given that there are 3 blue marbles, 2 white marbles, and 4 red marbles. Adding these quantities together gives us a total of 9 marbles in the box.

Step 3: Calculate probability of drawing a white marble

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, drawing a white marble is the favorable outcome.

Step 4: Substitute values for white marble probability

There are 2 white marbles and a total of 9 marbles. Therefore, the probability of drawing a white marble is $\frac{2}{9}$.

Step 5: Calculate probability of drawing a blue marble

Similarly, to find the probability of drawing a blue marble, we divide the number of blue marbles by the total number of marbles in the box.

Step 6: Substitute values for blue marble probability

There are 3 blue marbles and a total of 9 marbles. This gives a probability of $\frac{3}{9}$, which simplifies to $\frac{1}{3}$.

Step 7: Calculate probability of drawing a red marble

Finally, to find the probability of drawing a red marble, we divide the number of red marbles by the total number of marbles.

Step 8: Substitute values for red marble probability

There are 4 red marbles and a total of 9 marbles. Thus, the probability of drawing a red marble is $\frac{4}{9}$.

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