Question

find the probability that a bag contains 5 white,7 red and 3 black balls. if two balls are drawn one by one without replacement, find the probability of getting at least one ball as black?

Answer 1

The probability of drawing at least one black ball from a bag containing 5 white, 7 red, and 3 black balls when drawing two balls without replacement is 13/35.

Step-by-step explanation:

To find the probability of getting at least one black ball when two balls are drawn without replacement from the bag containing 5 white, 7 red, and 3 black balls, we can use complementary probability. The complementary event to 'getting at least one black ball' is 'getting no black balls', which means getting either white or red balls in both draws.

Let's calculate the probability of not getting a black ball in either of the two draws (getting only white or red balls), and then subtract this value from 1 to find the desired probability.

1. Calculate the total number of balls: 5 (white) + 7 (red) + 3 (black) = 15 balls.
2. Calculate the probability of drawing a white or red ball in the first draw: 12 (white or red balls) / 15 (total balls) = 4/5.
3. If the first ball was white or red, we now have 14 balls left. Calculate the probability of drawing a white or red ball in the second draw: 11 (remaining white or red balls) / 14 (remaining total balls) = 11/14.
4. Multiply the probabilities to find the combined probability of drawing two white or red balls: (4/5) * (11/14) = 44/70 = 22/35.
5. Subtract this probability from 1 to get the probability of getting at least one black ball: 1 - 22/35 = 13/35.

Therefore, the probability of drawing at least one black ball is 13/35.