There are 3 drawers in a dresser`, and you are equally likely to pick any of the three. In drawer 1, there are 2 black socks and 3 red socks. In drawer 2, there are 3 black socks and 2 red socks. In drawer 3, there are 3 black socks and 3 red socks. Once you have randomly selected a drawer, you randomly pull out a sock of that drawer.
- If you were to randomly choose a drawer and the draw two socks from that drawer, what is the probability that you get a pair (red or black)?
Where is my mistake:
P(R OR B|D1)= 2/5 * 3/4 = 3/10 P(R OR B|D2)= 3/5 * 2/4 = 3/10 P(R OR B|D3)= 1/2 * 1/2 = 1/4 P(R OR B)=P(R OR B|D1) P(D1) + P(R OR B|D2) P(D2) +P(R OR B|D3) P(D3)
The correct answer is 0.4, but if I use my work I can not reach that value. Can you help me to know where is my mistake? Thanks, comunity.