ii) A box contains 10 white, 7 black and 3 green balls. 2 balls are drawn at random. Find out the probability that: a) both are white
b) one is white and another is green
c) one is black and another is green
10/20 * 9/19
10/20 * 3/19
7/20 * 3/19
2 out of 10
To find the probability in each case, we need to first determine the total number of possible outcomes and the favorable outcomes.
Total number of possible outcomes:
When drawing 2 balls from the box, the total number of possible outcomes is given by the combination formula:
nCr = n! / (r! * (n-r)!)
where n is the total number of balls in the box and r is the number of balls drawn.
In this case, we have n=20 balls in total (10 white + 7 black + 3 green) and r=2 balls drawn.
So, the total number of possible outcomes is:
20C2 = 20! / (2! * (20-2)!) = 190
Now, let's calculate the favorable outcomes for each case:
a) Probability that both balls are white:
In this case, we want to select 2 balls from the 10 white balls. So, the number of favorable outcomes is:
10C2 = 10! / (2! * (10-2)!) = 45
Therefore, the probability of drawing 2 white balls is:
P(both white) = favorable outcomes / total outcomes = 45 / 190 ≈ 0.2368
b) Probability that one ball is white and another is green:
In this case, we want to select 1 white ball from the 10 white balls and 1 green ball from the 3 green balls. So, the number of favorable outcomes is:
10C1 * 3C1 = (10 * 3) = 30
Therefore, the probability of drawing 1 white and 1 green ball is:
P(1 white, 1 green) = favorable outcomes / total outcomes = 30 / 190 ≈ 0.1579
c) Probability that one ball is black and another is green:
In this case, we want to select 1 black ball from the 7 black balls and 1 green ball from the 3 green balls. So, the number of favorable outcomes is:
7C1 * 3C1 = (7 * 3) = 21
Therefore, the probability of drawing 1 black and 1 green ball is:
P(1 black, 1 green) = favorable outcomes / total outcomes = 21 / 190 ≈ 0.1105
So, the probabilities are:
a) P(both white) ≈ 0.2368
b) P(1 white, 1 green) ≈ 0.1579
c) P(1 black, 1 green) ≈ 0.1105