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.

So, 103/150 is correct.