Simplest way of approach


#1

there are 2 jars so the probability of selecting any one of two is 1/2 now coming to the jars since each jar must contain atleast 1 ball therefore, let jar 1 contains 1 red ball and jar 2 contains remaining 49 red and 50 blue balls i.e. total 99 balls. Now the probability of selecting a red ball is max in this case because if we have to pick a ball we will first select a jar out of 2 jars. Selecting 1 jar out of 2 available has the probability =1/2=0.5 so each jar has probability of 0.5. Now in jar 1 the probability of picking a red ball is 1/1=1 and the probability of picking a red ball in jar 2 is 49/100 =0.49. Now total probability is 0.51(jar 1 case) +0.50.49(jar 2 case)=0.75 (round off).
P.s.: Try thinking what would happen if we put >1 red ball in jar 1.