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junior college 1 | H1 Maths
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Need help for part(iii) and (iv) urgent!!
Date Posted: 4 years ago
Views: 573
10R, 8P, 7B
P (both are different colour)
= P(1st red, 2nd pink)
+ P(1st pink, 2nd red)
+ P(1st red, 2nd blue)
+ P(1st blue, 2nd red)
+ P(1st pink, 2nd blue)
+ P(1st blue, 2nd pink)
= 10/25 x 8/24
+ 8/25 x 10/24
+ 10/25 x 7/24
+ 7/25 x 10/24
+ 8/25 x 7/24
+ 7/25 x 8/24
= 2(10 x 8 + 10 x 7 + 8 x 7)/(25 x 24)
= 412/600
= 103/150
P (both are different colour)
= P(1st red, 2nd pink)
+ P(1st pink, 2nd red)
+ P(1st red, 2nd blue)
+ P(1st blue, 2nd red)
+ P(1st pink, 2nd blue)
+ P(1st blue, 2nd pink)
= 10/25 x 8/24
+ 8/25 x 10/24
+ 10/25 x 7/24
+ 7/25 x 10/24
+ 8/25 x 7/24
+ 7/25 x 8/24
= 2(10 x 8 + 10 x 7 + 8 x 7)/(25 x 24)
= 412/600
= 103/150
Alternatively, complement method :
P(both different colour)
= 1 - P(both same colour)
= 1 - P(both red) - P(both blue) - P(both pink)
= 1 - 10/25 x 9/24 - 7/25 x 6/24 - 8/25 x 7/24
= 1 - (10x9 + 7x6 + 8x7)/(25x24)
= 1 - 188/600
= 1 - 94/300
= 206/300
= 103/150
P(both different colour)
= 1 - P(both same colour)
= 1 - P(both red) - P(both blue) - P(both pink)
= 1 - 10/25 x 9/24 - 7/25 x 6/24 - 8/25 x 7/24
= 1 - (10x9 + 7x6 + 8x7)/(25x24)
= 1 - 188/600
= 1 - 94/300
= 206/300
= 103/150
Thank you, I got the same answer but the answer key showed 159/460
See 2 Answers
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I didn’t understand their method, is it wrong?
Date Posted:
4 years ago
Erm my answer was for iii), not iv)
Here's my working for iv) :
P(at least 2 red socks out of 3 now)
= P(all 3 red)
+ P(2 red, 1 other colour)
= P(all 3 red)
+ P(1st red, 2nd not red, 3rd red)
+ P(1st red, 2nd red, 3rd not red)
+ P(1st not red, 2nd red, 3rd red)
= 10/25 x 9/24 x 8/23
+ 10/25 x 15/24 x 9/23
+ 10/25 x 9/24 x 15/23
+ 15/25 x 10/24 x 9/23
= (10x9x8 + 3x10x15x9)/(25 x 24 x 23)
= 4770/13800
= 477/1380
= 159/460
P(at least 2 red socks out of 3 now)
= P(all 3 red)
+ P(2 red, 1 other colour)
= P(all 3 red)
+ P(1st red, 2nd not red, 3rd red)
+ P(1st red, 2nd red, 3rd not red)
+ P(1st not red, 2nd red, 3rd red)
= 10/25 x 9/24 x 8/23
+ 10/25 x 15/24 x 9/23
+ 10/25 x 9/24 x 15/23
+ 15/25 x 10/24 x 9/23
= (10x9x8 + 3x10x15x9)/(25 x 24 x 23)
= 4770/13800
= 477/1380
= 159/460
My bad I send the wrong part
Even for part(iv),
Shouldn’t it be
P(all 3 red)
+ P(1st red x 2nd red x 3rd pink)
+ P(1st red x 2nd red x 3rd blue)
+ P(1st pink x 2nd red x 3rd red)
+ P(1st blue x 2nd red x 3rd red)
Shouldn’t it be
P(all 3 red)
+ P(1st red x 2nd red x 3rd pink)
+ P(1st red x 2nd red x 3rd blue)
+ P(1st pink x 2nd red x 3rd red)
+ P(1st blue x 2nd red x 3rd red)
At least 2, and there are different probabilities when I first pick red, blue or pink socks
Yes, but realise something : you've missed out these probabilities.
P(1st red, 2nd blue, 3rd red)
P(1st red, 2nd pink, 3rd red)
P(1st red, 2nd blue, 3rd red)
P(1st red, 2nd pink, 3rd red)
Ah thank you
What I did in my working was , instead of separately computing the cases with ① 2 reds 1 pink and ②2 reds 1 blue,
I choose to combine them together and do the various orders of 2 red, 1 non-red
(Non-red already covers both pink and blue)
You can try to do for the separate case and you should still get 159/460
I choose to combine them together and do the various orders of 2 red, 1 non-red
(Non-red already covers both pink and blue)
You can try to do for the separate case and you should still get 159/460
Edited
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Part(iii)
Date Posted:
4 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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