Jar 1 has 2 red marbles and 4 white marbles Jar 2 has 3 red

Jar #1 has 2 red marbles and 4 white marbles. Jar #2 has 3 red marbles and 1 white marble. JAR #3 has 2 red marbles and 3 white marbles. One marble is randomly taken from jar #1 and put into jar #2. One marble is then randomly taken from jar #2 and put into jar #3. If one marble is randomly selected from jar #3, what is the probability it will be red? Hint: Make a tree diagram of the sequence of events.

Please include all steps with the answer

Solution

Jar I --   2 red marbles and 4 white marbles

          If marble is red --- Prob 1/3    ...    Jar 2 would have 4 red and 1 white marble           

                                          .. From jar 2 if red is selected (Prob 4/5)  

                                                                             -- Jar 3 would have 3 red and 3 white marbles.

                                   Prob for red in this series = 3/6 = 1/2

         If marble is white -- Prob 2/3 ... Jar 2 would have 3 red and 2 white marble     

   If red marble is selected with prob 3/5 and put into jar 3,