Question: a bag containing 3 red balls ,4 white balls and two blue balls .if a ball is chosen at a random what is the probability that it is a red ball
1. **State the problem:** We have a bag with $3$ red balls, $4$ white balls, and $2$ blue balls. We want to find the probability of randomly selecting a red ball.
2. **Formula for probability:** The probability of an event is given by:
$$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$
3. **Calculate total number of balls:**
$$3 + 4 + 2 = 9$$
4. **Number of favorable outcomes:** The favorable outcomes are the red balls, which is $3$.
5. **Calculate probability:**
$$\text{Probability} = \frac{3}{9}$$
6. **Simplify the fraction:**
$$\frac{\cancel{3}}{\cancel{9}} = \frac{1}{3}$$
7. **Final answer:** The probability of choosing a red ball is $\frac{1}{3}$.
This means if you randomly pick a ball from the bag, there is a one in three chance it will be red.