Question

Q8. Three balls are drawn a random without replacement from a box containing 8 white, 4 black, and 4 red balls. Calculate the probabilities that there will be [4]

a) at least one white ball;
b) two white balls and one black ball;
c) two balls of one color and the other of a different color;
d) one ball of each color.

Answer 1

(8) There are 16 balls in the bag of which 8 White, 4 Black, and 4 Red. So from these 16 balls 3 balls can be drawn in ways.

So, the total number of elementary events =

(a) At least one white ball: There are 8 white balls and to draw at least one white balls mean, there can be one white ball and the other two are black & red ball, two white ball and the other one is black or red and finally, it can also be three white balls.

So, at least one white ball can be drawn in :

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(b) Two white balls and one black ball: There are 8 White balls and 4 black balls, so two white balls and one black ball is drawn in-

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(c)Two balls of one color and the other of a different color: Two balls of one color and other ball of different color can be drawn as-

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(d) One ball of each color: The number of ways in which one ball of each color can be drawn is: