Total number of chips = 4+ 6 = 10
Number of white chips = 4
Probability of picking a white chip =

This white chip is not replaced back into the bag. This will reduce the number of white chips in the bag by 1 and reduce the total number of chips in the bag by 1.
So, now the total number of chips in the bag = 3 + 6 = 9
Number of white chips in the bag = 3
Probability of picking a white chip =

Thus, the probability of picking two white chips will be =
Therefore, option B gives the correct answer.