Boxes 1 and 2 contain 4 white, 3 red and 3 blue balls; and 5 white, 4 red and 3 blue balls respectively. If one ball is drawn at random from each box, what is the probability that both the balls are of the same colour?
[Math] one ball is drawn at random from each box, what is the probability that both the balls are of the same colour
probability
Best Answer
This problem is a short calculation. Since both of the draws from the boxes are independent events, the probability of drawing a color from one box and the same color from the other box can be multiplied to find the probability of both events happening. Since the probability of drawing each color is disjoint from the other, the probability of the same color is the sum of the probability of drawing each color.
$P(\mbox{A and B})$ $=$ $P(A)P(B)$ if the events are independent.
$P(\mbox{A or B})$ $=$ $P(A)+P(B)$ if the events are disjoint.
$P(\mbox{2 whites}) = P(\mbox{white from the first box}) P(\mbox{white from the second box}) = \frac{4}{10} * \frac{5}{12} = \frac{20}{120}=\frac{1}{6}$
Similarly, $P(\mbox{2 reds}) =\frac{3}{10} * \frac{4}{12}=\frac{1}{10}$ and $P(\mbox{2 blues}) =\frac{3}{10} * \frac{3}{12} = \frac{3}{40}$
$P(\mbox{same color})=P(\mbox{2 whites})+P(\mbox{2 reds})+P(\mbox{2 blues})=\frac{41}{120}$
Edited for answer twice.