Question

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

Answer 1

According to the question we have to determine the probability that a marble is drawn at random from the box is (i) white (ii) blue and or (iii) red. So, first of all we have to understand about the probability which is as explained below:
Probability: To determine the probability first of all we have to divide the required event by the sample space or we can say that the total number of possible outcomes.
Now, we have to determine the probability for when the white marble is drawn from the box in which first of all we have to determine the required white marbles and then the total number of marbles in the box.
Now, the same as we have to determine the probability for when the blue marble is drawn from the box in which first of all we have to determine the required blue marbles and then the total number of marbles in the box.
Now, the same as we have to determine the probability for when the red marble is drawn from the box in which first of all we have to determine the required red marbles and then the total number of marbles in the box.

Complete step-by-step solution:
Step 1: First of all we have to determine the number of white balls with the help of probability as explained in the solution hint so, first of all as mentioned in the question that 2 white balls are drawn at random so, this is our required event and our sample space is 9. Hence,
$= \dfrac{2}{9}$
Step 2: Now, we have to determine the number of blue balls with the help of probability as explained in the solution hint so, first of all as mentioned in the question that 4 red balls are drawn at random so, this is our required event and our sample space is 9. Hence,
$= \dfrac{3}{9} \\\ = \dfrac{1}{3}$
Step 3: Now, we have to determine the number of red balls with the help of probability as explained in the solution hint so, first of all as mentioned in the question that 3 blue balls are drawn at random so, this is our required event and our sample space is 9. Hence,
$= \dfrac{4}{9}$

Hence, we have obtained the probabilities when 2 white marbles are drawn at random from the box is $= \dfrac{2}{9}$, 3 blue marbles are drawn at random from the box is $= \dfrac{1}{3}$ and 4 red marbles are drawn at random from the box is $= \dfrac{4}{9}$.

Note: To determine the probability first of all we have to divide the required event by the sample space or we can say that the total number of possible outcomes.
Probability of any event can’t be zero; it is always in the form of a fraction.