Two bags A and B have equal numbers of balls. Bag A has 20% red balls 80% green balls. Bag B has 30% red balls, 60% green balls and 10% yellow balls. Contents of Bags A and B are mixed thoroughly, and a ball is randomly picked from the mixture. What is the chance that the ball picked is red?

To find the chance that the ball picked is red from the mixture, we need to determine the total number of red balls and the total number of balls in the mixture. The problem states that bags A and B have an equal number of balls. Let's assume a convenient number for the total balls in each bag to simplify calculations, for example, 100 balls in each bag.

Total Balls Calculation

Since both bags A and B have an equal number of balls, we can assume a specific number of balls in each bag. Let's consider 100 balls in each bag for easier percentage calculations.

- Balls in Bag A = 100
- Balls in Bag B = 100

The total number of balls when the contents of Bag A and Bag B are mixed will be the sum of balls from both bags.

- Total balls in mixture = Balls in Bag A + Balls in Bag B
- Total balls in mixture = $100+100=200$ balls

Red Balls in Each Bag

Next, we calculate the number of red balls contributed by each bag based on their given percentages.

Red Balls in Bag A

Bag A has 20% red balls.

- Red balls in Bag A = $20\%\text{ of }100$
- Red balls in Bag A = $\frac{20}{100}\times 100=20$ red balls

Red Balls in Bag B

Bag B has 30% red balls.

- Red balls in Bag B = $30\%\text{ of }100$
- Red balls in Bag B = $\frac{30}{100}\times 100=30$ red balls

Total Red Balls in Mixture

The total number of red balls in the mixture is the sum of red balls from Bag A and Bag B.

- Total red balls = Red balls in Bag A + Red balls in Bag B
- Total red balls = $20+30=50$ red balls

Chance of Picking a Red Ball

The chance (or probability) of picking a red ball from the mixture is calculated by dividing the total number of red balls by the total number of balls in the mixture.

Probability of picking a red ball = $\frac{\text{Total number of red balls}}{\text{Total number of balls in mixture}}$

Probability of picking a red ball = $\frac{50}{200}$

Probability of picking a red ball = $\frac{1}{4}$

Converting to Percentage

To express this chance as a percentage, we multiply the fraction by 100.

Percentage chance = $\frac{1}{4}\times 100\%$

Percentage chance = $25\%$

Therefore, the chance that the ball picked is red is 25%.