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

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)

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)

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

Edited