Answer:
1/9
Explanation:
Well the chance of picking 3 one time is 1/3
The chance of picking 3 the second time is 1/3
So at first, we've succeeded with probability 1/3 and failed with probability 2/3
We don't care what happens next if we've failed - we already failed.
So we've reached the "picking the second card with hope in our hearts" 1/3 of the time and we again succeed with 1/3 of a chance, so the total probability of success is 1/3 * 1/3 = 1/9
Think of the options:
3 and 3 - probability 1/3 * 1/3 = 1/9
3 and non-3 - probability 1/3 * 2/3 = 2/9
non-3 and 3 - probability 2/3 * 1/3 = 2/9
non-3 and non-3 - probability 2/3 * 2/3 = 4/9
Note that all the options sum to 1 - as probabilities of all options always should.