Question

A bag contains 5 red and 7 black balls. A ball is drawn at random from the bag, the color is noted and the ball is replaced. A second ball is then drawn. Find the probability that the first ball is red and the second is black.

Answer 1

$$5+7=12$$

$$P(first\ red\ \& second \ black)=\dfrac{5}{12}(\dfrac{7}{12})=\dfrac{35}{144}$$

The probability that the first ball is red and the second is black is $\dfrac{35}{144}.$