A bag contains 8 red and 5 white balls. If 3 balls are drawn randomly then find the probability that one ball of Red colour and two balls of white colour are drawn? average after six innings? other side working together can finish the work?

Given:

• Total red balls = 8

• Total white balls = 5

• Total balls = 8 + 5 = 13

• Number of balls drawn = 3

• Condition: 1 red ball and 2 white balls

Concept Used:

To calculate the probability of an event, we use the formula:

Probability = (Number of favorable outcomes) / (Total possible outcomes)

The total number of ways to choose 3 balls from 13 is given by:

Total combinations: C(13, 3) = 13! / (3! × (13 - 3)!)

For favorable outcomes:

Choose 1 red ball out of 8: C(8, 1) = 8

Choose 2 white balls out of 5: C(5, 2) = 5! / (2! × (5 - 2)!)

Calculation:

Total possible outcomes:

C(13, 3) = 13! / (3! × 10!) = (13 × 12 × 11) / (3 × 2 × 1)

⇒ C(13, 3) = 286

Favorable outcomes:

C(8, 1) = 8

C(5, 2) = 5! / (2! × 3!) = (5 × 4) / (2 × 1)

⇒ C(5, 2) = 10

Total favorable outcomes = C(8, 1) × C(5, 2) = 8 × 10 = 80

Probability:

P = Favorable outcomes / Total outcomes

⇒ P = 80 / 286

Simplify:

⇒ P = 40 / 143

Conclusion:

The probability of drawing 1 red ball and 2 white balls is: 40 / 143

∴ The correct answer is Option 2.