Question

Cameron has a bag that contains one silver and one gold marble the Marvels are the same size. Cameron chooses one marble at random and then puts it back in the bag then he chooses the second marble the outcome is GS means that gold marble was chosen first and the silver marble was chosen second move out comes to the line to complete the tree diagram the move numbers to the boxes to correctly label each outcome with its probability

Answer 1

Notice that the probability of an event to happen is the ratio between the favorable outcomes divided the total possible outcomes.

So, when one picks a marble from the bag that contains just two marbles, the chance of getting one that is the silver, is 1/2 because the favorable events are just one (the only silver marble) and the total possibilities is 2 (the two possible marbles)

Therefore, when we complete the table, for the first path:

First draw silver, the probability is 1/2 then putting back the marble in the bag, and picking one again this being now the gold one, is also 1/2.

When we have these repeated event, the probabilities of each step multiply:

Then for this frist branch:

S (first) ---> G (second) --> 1/2 * 1/2 = 1/4 = 0.25

For the second path:

S (first) ---> S (second) ---> 1/2 * 1/2 = 1/4 = 0.25

Notice as we go that since we always pick one possible outcome from a bag with two marbles, we always have in each picking event a probability of 1/2.

For the third path:

G (first) ---> S (second) --> 1/2 * 1/2 = 1/4 = 0.25

For the fourth path:

G (first) ---> G (second) --> 1/2 * 1/2 = 1/4 = 0.25

Now, we can add the final probabilities to make sure we covered all possible situations. Whenyou add the probabilities of all possible outcomes , you should always get "1" (one). We see that is the case for us, since the addition of four fractions 1/4 gives one.