How will divide the pearls to increase your chances of survival?

Question

You are trapped into a death trap by the famous jigsaw killer. A screen flashes in front of you and explains you the trap game.

There are 100 pearls kept in a bowl in front of you and an empty bowl. Among the 100 pearls, 50 are white and 50 are black. You can divide them as you like into the two bowls. Once you are done, you will pull a lever, which will turn the room pitch black. The bowls will move and shuffle around. In the dark, you have to pick up one pearl from any bowl. Once you do that, the room will flood with lights again. If the peral you have in your hand is white, you will be allowed to live, but if the pearl you picked is black, the room will be filled with poisonous gas and you will die.

How will divide the pearls to increase your chances of survival?

Answer 1

Put 1 white pearl in one bowl and remaining 49 white pearls plus 50 black pearls in other bowl.

Then probability of getting white ball from first bowl is 1/1 = 1
Probability of getting 1 white pearl from second bowl is 49/99 = 0.49

Therefore total probability of getting a white pearl from one bowl at random will be,
0.5 x 1 + 0.5 x 0.49 = 0.745

Therefore, there will be a chance of living will be 74.5%

Answer 2

Place one white pearl in a bowl and all the rest into another bowl.

Then probability of getting white ball from first bowl is 1/1 = 1
Probability of getting 1 white pearl from second bowl is 49/99 = 0.495

Probability of picking the white ball
0.5 x 1 + 0.5 x 0.49 = 0.745

Answer 3

Answer:
Put 1 white pearl in one bowl and remaining 49 white pearls plus 50 black pearls in other bowl.
Then probability of getting white ball from first bowl is 1/1 = 1
Probability of getting 1 white pearl from second bowl is 49/99 = 0.49

Therefore total probability of getting a white pearl from one bowl at random will be,
0.5 x 1 + 0.5 x 0.49 = 0.745

Therefore, there will be a chance of living will be 74.5%