Can someone explain this

Letting the first die be blue, try listing all the outcomes that satisfy the given conditions.

Blue can't be 1 .... why not?
If blue is 2, then red must be 6 ... why?
If blue is 3, then red could be 5 or 6.
If blue is 4, then red could be 4 or 5 or 6.
Blue can't be 5 or 6 .... why not?

The notation P(sum >7) is actually incorrect. It should be P(sum >7 | blue die is less than 5) where | reads "given that".
Have you learnt about conditional probability?
 
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