The security passes for a certain company are coloured yellow or white, they're provided with either a clip or a chain. The probability that a pass has a clip is 6/10, 2/3 of the white passes and 4/7 of the yellow ones are fitted with clips. A member of the company is stopped on his way into work find the probability that;
The pass is yellow
The pass is yellow with a chain
If two people are stopped randomly as they enter find the probability that one pass will be yellow and the other white, and one will have a clip and the other a chain.
The Attempt at a Solution
Really frustrating question, is this question possible? :/ This is what I've tried, but it's wrong according to the book;
(3/7 * 4/10) + (4/7 * 6/10) = 0.514 (I know this is wrong but I was trying anything)
I just don't see how this is possible because surely it's dependant on the actual number that are white and yellow? Surely if there's 1000 white, and 5 yellow, the probability of a yellow is much different than with different numbers there, and they tell you no-where what to assume...
Any help would be great.