QN's answer to QN's Junior College 1 H1 Maths Singapore question.
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Part(iii)
Date Posted:
3 years ago
This answer has two mistakes.
They stated P(both same colour)
= 2/5 x 3/8 + 8/25 x 5/12 + 7/25 x 5/12
① Only the first product of fractions is correct.
2/5 x 3/8 was actually simplified from 10/25 x 9/24.
The 10/25 referred to 10 reds out of all 25 socks for the 1st sock taken.
The 9/24 referred to 9 reds out of 24 remaining socks for the 2nd sock taken.
So this = P(both are red) ✓
BUT,
② 8/25 x 5/12 is wrong.
8/25 x 5/12 was simplified from 8/25 x 10/24.
The 8/25 referred to 8 pinks out of all 25 socks for the 1st sock taken.
The 10/24 referred to 10 reds out of 24 remaining socks for the 2nd sock taken
This probability = P(1st pink,2nd red). But the correct one should have been P(both pink)
Likewise,
③ 7/25 x 5/12 is also wrong.
7/25 x 5/12 was simplified from 7/25 x 10/24.
The 7/25 referred to 7 blues out of all 25 socks for the 1st sock taken.
The 10/24 referred to 10 reds out of 24 remaining socks for the 2nd sock taken
This probability = P(1st blue,2nd red) , not P(both blue) when it should have been.
They stated P(both same colour)
= 2/5 x 3/8 + 8/25 x 5/12 + 7/25 x 5/12
① Only the first product of fractions is correct.
2/5 x 3/8 was actually simplified from 10/25 x 9/24.
The 10/25 referred to 10 reds out of all 25 socks for the 1st sock taken.
The 9/24 referred to 9 reds out of 24 remaining socks for the 2nd sock taken.
So this = P(both are red) ✓
BUT,
② 8/25 x 5/12 is wrong.
8/25 x 5/12 was simplified from 8/25 x 10/24.
The 8/25 referred to 8 pinks out of all 25 socks for the 1st sock taken.
The 10/24 referred to 10 reds out of 24 remaining socks for the 2nd sock taken
This probability = P(1st pink,2nd red). But the correct one should have been P(both pink)
Likewise,
③ 7/25 x 5/12 is also wrong.
7/25 x 5/12 was simplified from 7/25 x 10/24.
The 7/25 referred to 7 blues out of all 25 socks for the 1st sock taken.
The 10/24 referred to 10 reds out of 24 remaining socks for the 2nd sock taken
This probability = P(1st blue,2nd red) , not P(both blue) when it should have been.
So, 103/150 is correct.
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