I am still confused about why you can conclude that P(a)> = 0.6 and P(b)> = 0.6?
The only thing we know for sure is that the probability of both A and B is 0.6. We can then take the equation P(A & B) = P(A) x P(B). So again, we know that P(A & B) = 0.6. I think the best way to explain this would be to plug in numbers and see what we get.
We know that the probability of something cannot be greater than 1, so P(A) < 1. We also know that the probability of A must be greater than zero, because P(A & B)= 0.6. So, we know 0 < P(A) < 1. Now let's plug in some numbers.
If, for example, P(A) = 0.4, we would have the equation 0.6 = 0.4 x P(B). This would make P(B) = 1.5, which we know isn't possible. And if P(A) = 0.5? P(B) would equal 1.2 (again, not possible). Let's try 0.6. 0.6 = 0.6 x P(B). P(B) would equal 1. That's possible! So, now we know that the probability of both A and B must be greater than 0.6, otherwise the other probability will be greater than 1.
Thus, the probability that event A occurs is greater than 0.6, and therefore greater than the quantity in column B (0.3).