Maths probability question help

enoassap SG

Hello, I need some help with a certain probabiltiy question that is really annoying me.

There are 30 pens in total, 20 of them are black and 10 of them are blue.
Of the 20 Black pens, 8 dont work, while the other 12 work.
Of the 10 Blue pens, 6 dont work, while the other 4 work.

What is the probabilty of picking two pens (no replacement) that are of the same colour and are also working at the same time?

I cant figure out how to do the 'and also working' part correctly!!!!!!!#*#)($#

Garrick_3658 SG

Hard at work early in the morning? Take a break

Black - 20/30

Working - 12/20

Blue - 10/30

Working - 4/10

I'm assuming picking 2 pens ONE AFTER ANOTHER, if it's AT THE SAME TIME then make the necessary changes on your own (which I guess, is doable)

1st Black and working - 20/30 x 12/20 = 2/5

2nd Black and working - 19/29 x 11/19 = 11/29

Black and working = 2/5 x 11/29 = 22/145

Blue and working = 10/30 x 4/10 x 9/29 x 3/9 = 2/145

Probability = 22/145 + 2/145 = 24/145

Haven't done probability in a long time. Better get someone to re-confirm first.

Forbiddensinner SG