M
Mathematics , 17.02.2022 17:53

Cameron has a bag that contains one silver (S) and one gold (G) marble. The marbles are the same size. Cameron chooses one marble at random and then puts it back in the bag. Then he chooses a second marble. The outcome "GS" means that a gold marble was chosen first and
a silver marble was chosen second.
Move outcomes to the lines to complete the tree diagram. Then, move numbers to the boxes to correctly label each outcome with its
probability.

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First, we have two marbles, and i guess that each one has the same probability of being picked at random (actually they have different densities, so one may have a larger probability than the other).

The possible outcomes are:

S G

S S

G S

G G

Now, suppose that we want to find the probability of the S G outcome.

In the first selection, we want to pick the silver marble, with a probability of ps,

In the second selection, we want to pick the gold marble, with a probability pg

As the events are independent, the joint probability will be equal to the product of the probabilities for each selection:

P = ps*pg

Now, if both marbles have the same probability of being picked, then:

ps = 0.5

pg = 0.5

P = 0.5*0.5 = 0.25

And this will be the same for each outcome.

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