Question

two bags each contain ten discs which are indistinguishable apart from their colour. The first bag contains 4 red and 6 black discs and the second, 7 red and 3 black discs. A disc is chosen at random from the first bag and placed in the second. bag and placed in the first. Find the probability that the first bag still contains exactly 4 red discs?

Answer 1

Let $E_1$ denote bag 1 ams $E_2$ demote bag 2

$P(E_1)=P(E_2)=\dfrac{1}{2}$

Let A denote the probability of red discs

Probability of drawing black balls from bag 1=$\dfrac{6}{10}=0.6$

probability that the first bag still contains exactly 4 red discs

=$\dfrac{P(E_1)(0.6)}{P(E_1)(0.6)+P(E_2)(0.4)}=\dfrac{0.3}{0.2+0.3}=\dfrac{0.3}{0.5}=0.6$