There are two bags. First contains 7 red and 5 violet balls whereas second contains 7 violet and 5

Probability of get one red from one bag and one violet from another bag = [(7/12)*7/12)]+[(5/12)*(5/12)] = 74/144,
Now, Probability of both balls having same color = 1/(74/144)=70/144=35/72

Thanks for making necessary correction in the question.
Probability of both balls having violet colour is 5/12 *7/12.
Probability of both balls having red colour is 5/12 *7/12.
Probability of both balls having same colour is
5/12 *7/12 + 5/12 *7/12
or
2*5/12 *7/12 =35/72

( 7/12*5/12) +(5/12*7/12)

probability of 2 red balls = 7/12 x 5/12
probability of 2 violet balls = 7/12 x 5/12
probability of 2 balls of same color =2x 7/12 x 5/12 = 35/72

For this corrected statement

probability of 2 balls of same colour ( 2red or 2 violet ) = 2x7/12 x 5/12 =35/72

P(Choosing same color ball)

= P (Choosing both red) OR P (Choosing both violet)

= P(R from first) and P(R from second) + P(V from first and P(V from second)

= (7/12)(5/12) + (5/12)(7/12)

= 2 (35/144)

= 35/72

both red or both violet
7/12*5/12+5/12*7/12

Probability of both balls having same colour is= (5/12)*(7/12)+(7/12)*(5/12)= (35/144)+(35/144)= (70/144) or, (35/72)...... Option 5)

First if the balls are red, then probability is 7/12*5/12, similarly if both are violet it is 5/12*7/12 adding both probabilities we get total prob of both balls being of same colour as 35/144+35/144 = 35/72

There are two possibilities here. Either both balls should be red or both should be violet.
1)First consider probability for getting 2 red balls. From the first bag there are 7 red balls in a total of 12 balls. So the probability of picking a red ball is 7/12. Similarly the probability of picking a red ball from 2nd bag is 5/12.Since these should occur concurrently we have to multiply both values.Then it is 35/144.
2)Now apply the same process for violet balls. There are 5 violet balls in 1st bag in a total of 12 balls. So the probability of picking a violet balls is 5/12. Similarly from the 2nd bag it is 7/12. Multiply these values again you get 35/144. Now either of these results can occur so add the values. 35/144 + 35/144 = 35/72