Question

Two balls are drawn from a bag containing 3 red, 3 green and 4 black balls. Find the probability that :

(a)both are red,

(b)one is green and one is black,

(c)both are of the same colour.

Answer 1

The probability of drawing two red balls is 1/15, the probability of drawing one green ball and one black ball is 4/15, and the probability of drawing two balls of the same color is 11/15.

Step-by-step explanation:

To find the probabilities, we need to know the total number of balls in the bag and the number of balls of each color. In this case, the bag contains 3 red balls, 3 green balls, and 4 black balls. We can use these numbers to calculate the probabilities:

(a) Probability of drawing two red balls = (Number of red balls / Total number of balls) * (Number of red balls - 1 / Total number of balls - 1) = (3/10) * (2/9) = 1/15

(b) Probability of drawing one green ball and one black ball = (Number of green balls / Total number of balls) * (Number of black balls / Total number of balls - 1) + (Number of black balls / Total number of balls) * (Number of green balls / Total number of balls - 1) = (3/10) * (4/9) + (4/10) * (3/9) = 12/90 + 12/90 = 4/15

(c) Probability of drawing two balls of the same color = Probability of drawing two red balls + Probability of drawing two green balls + Probability of drawing two black balls = 1/15 + 4/15 + 6/15 = 11/15