Chess Probability of two white knights being on black squares or

Devi

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A chess board has 64 squares, 32 white and 32 black, and is played with 16 black and 16 white pieces. If all the pieces are placed randomly on the board, what is the probability of two white knights being on black squares or a black bishop being on a black square?

The answer is .726 not 13/16. I just don’t know how to get it.
 
Welcome to the forum Devi,

As per forum guidelines (and just because it makes sense), please show us your work. What have you tried so far? How did you end up with 13/16? We can't help you if we can't see where you're going wrong.

The pieces being arranged randomly implies that all configurations are equally likely. If that's true, then the probability of a given arrangement is

(number of ways to make desired arrangement) / (total number of arrangements).

What is the total number of arrangements? You have 64 spots onto which to place 32 pieces. The "ordering" of the pieces (which piece goes in which spot) matters, because the pieces are distinguishable from each other. So would that be perhaps 64 permute 32 = 64!/32! ???

What about the number of desired outcomes? How many ways are there to place two white knights on two black squares? Start with that.
 
A chess board has 64 squares, 32 white and 32 black, and is played with 16 black and 16 white pieces. If all the pieces are placed randomly on the board, what is the probability of two white knights being on black squares or a black bishop being on a black square?

The answer is .726 not 13/16. I just don’t know how to get it.
You need to know that p( A or B) = P(A) + P(B) - P(A int B). Let A= two white knights being on black squares. B = a black bishop being on a black square.

Can you compute P(A), P(B) and P(A int B)? You might need another formula to compute P(A int B).

Please show us your work so we can see where you are having trouble. I started you off in case you were stuck at the beginning.
 
There are 2^4 ways of possible outcomes and 13 of those has two white knights on black squares, at least one black bishop being on a black square, and if both are correct. 13/16 equals .8125 but that’s not the correct answer. I think I’m misunderstanding or not counting for a part in the question, but I just don’t know which part. It’s confusing, and I tried not including the “and” and accounting for only 1 black bishop on a black square but no luck. The book says .726...maybe it’s a typo or another advanced way of understanding the question and approaching it differently, but I aren’t learned it yet.
 
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