Red Blue marble - probability puzzle

We have 50 red marbles, 50 blue marbles and 2 jars. 
One of the jars is chosen at random and then one marble will be chosen from that jar at random. 
How would you maximize the chance of drawing a red marble? What is the probability of doing so? 
All 100 marbles should be placed in the jars.
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Answer:
Put a single Red marble in one jar. And rest of 99 in other jar.
Which gives the maximum probability.
= ((1/2)*1)  +  (( 1/2)*(49/99))
= 0.50 + 0.2474
= 0.7474
= 0.75 or 75%