A ba contains 5 red and 4 white identical balls abd a second bag contains 3 red and white identical balls
If one ball ios selected at random from each of the bags,
Find the probability that, two balls selected will be of
I)different colour
Ii)same colour
Assuming bag2 contains 3 red and 3 white balls,
P(r,r) = 5/9 * 1/2
P(w,w) = 4/9 * 1/2
so, 1/2
seems strange, no?
But think. No matter what color ball you pick from bag #1, there is a 50-50 chance that the ball from bag2 will match it.
If I got the ball count wrong for bag2, just adjust the 2nd probabilities above.
To find the probability of selecting different color balls, we need to consider all possible combinations where one ball is red and the other ball is white.
I) Different Color:
The number of ways to select a red ball from the first bag and a white ball from the second bag is 5 (red) * 3 (white) = 15.
Similarly, the number of ways to select a white ball from the first bag and a red ball from the second bag is 4 (white) * 3 (red) = 12.
Therefore, the total number of ways to select different color balls is 15 + 12 = 27.
The total number of possible outcomes is the product of the number of balls in each bag, which is 9 (total number of balls in the first bag) * 6 (total number of balls in the second bag) = 54.
To find the probability, we divide the number of ways to select different color balls (27) by the total number of possible outcomes (54):
Probability of selecting different color balls = 27/54 = 1/2 or 0.5.
II) Same Color:
The number of ways to select a red ball from the first bag and a red ball from the second bag is 5 (red) * 3 (red) = 15.
Similarly, the number of ways to select a white ball from the first bag and a white ball from the second bag is 4 (white) * 3 (white) = 12.
Therefore, the total number of ways to select same color balls is 15 + 12 = 27.
The total number of possible outcomes is the product of the number of balls in each bag, which is 9 (total number of balls in the first bag) * 6 (total number of balls in the second bag) = 54.
To find the probability, we divide the number of ways to select same color balls (27) by the total number of possible outcomes (54):
Probability of selecting same color balls = 27/54 = 1/2 or 0.5.