Probability?

Let P( X , Y ) denote P( Coin 1 tossed X , Coin 2 tossed Y )
P( H H ) = 0.492*0.579 = 0.284868
P( H T ) = 0.492*0.421 = 0.207132
P( T H ) = 0.508*0.579 = 0.294132
P( T T ) = 0.508*0.421 = 0.213868

(1)
P( exactly 1H | at least 1H )
= P( exactly 1H ∩ at least 1H ) / P( at least 1H )
= P( exactly 1H ) / P( at least 1H )
= [ P( H T ) + P( T H ) ] / [ P( H H ) + P( H T ) + P( T H ) ]
= ( 0.207132 + 0.294132 ) / ( 0.284868 + 0.207132 + 0.294132 )
≒ 0.638 ..... Ans

(2)
P( exactly 1T | at least 1T )
= P( exactly 1T ∩ at least 1T ) / P( at least 1T )
= P( exactly 1T ) / P( at least 1T )
= [ P( H T ) + P( T H ) ] / [ P( H T ) + P( T H ) + P( T T ) ]
= ( 0.207132 + 0.294132 ) / ( 0.207132 + 0.294132 + 0.213868 )
≒ 0.701 ..... Ans