Question

A bag contains 5 red and 4 black balls. A ball is drawn at random from the bag. What the probability of getting a black ball ?​

Answer 1

Answer:

Given,

• Bag1 → 5 red , 4 black balls and
• Bag2 → 3 red , 7 black balls.

Firstly a ball is picked from Bag1 in random.

Case1: Pick a red from Bag1 with probability, 5/(5+4) = 5/9

Bag2 now has 4 red and 7 black from which a ball is picked in random. A red can be picked with probability, 4/(4+7) = 4/11. Since these being dependent tasks must be added for the actual probability,

5/9 * 4/11 → {1}

Case2: Pick a black from Bag1 with probability, 4/(5+4) = 4/9

Bag2 now has 3 red and 8 black from which a ball is picked in random. A red can be picked with probability, 3/(4+7) = 3/11. Since these being dependent tasks must be added for the actual probability,

4/9 * 3/11 → {2}

Now both these cases are dependent. Thus their probabilities must be added. Thus the probability of picking red from Bag2 is,

(5/9*4/11) + (4/9*3/11) = 32/99.

Answer 2

Answer:

Probability of getting a black ball is 4/9.

Step-by-step explanation:

Bag contains 5 red and 4 black balls.

Total number of balls = 9

By using the formula for probability,

P(E) = (Number of possible outcomes) / (Total number of outcomes)

P(Black) = (Number of black balls) / (Total number of balls)

             = 4 / 9

Thus, probability of getting a black ball is 4/9.