Probability problem

別性別岐視好嗎? Maths 5** 的師姐大有人在呢~
P(the ball from the first box is black | the two balls are of different colours)
= P(the ball from the first box is black but the ball from the second box is not)
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　　　　　　　　P(the two balls are of different colours)
= P(the ball from the first box is black and the ball from the second box is green or yellow)
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　　　　　　　　P(the two balls are of different colours)
=　　　4/(4+5+1) × (5+3)/(4+5+3)
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1 - P(the two balls are the same colour)

=　　　　　　4/(4+5+1) × (5+3)/(4+5+3)
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1 - P(2 black balls) - P(2 green balls) - P(2 yellow balls)

=　　　　　　　　　　　4/(4+5+1) × (5+3)/(4+5+3)
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1 - 4/(4+5+1) × 4/(4+5+3) - 5/(4+5+1) × 5/(4+5+3) - 1/(4+5+1) × 3/(4+5+3)

= 　　　　　　　4/10 × 8/12
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1 - 4/10 × 4/12 - 5/10 × 5/12 - 1/10 × 3/12

=　　　　　4 × 8
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120 - 4 × 4 - 5 × 5 - 1 × 3