Question

suppose 4 green and 5 red identical objects are in a jar. a blindfolded person randomly selects two of these objects from the jar one after another, without replacing them back into the jar. the following tree diagram depicts all the possible random outcomes and their probabilities. note: please enter your answers below in simplified fraction form. a) what is the conditional probability ( p ( red | green ) = )? b) what is the probability of obtaining a final outcome with two green objects?

Explanation:

Step1: Identify the path for two green objects

The probability of first picking a green object is $\frac{4}{9}$. After picking one green object, there are 3 green objects left out of 8 total objects. So the probability of then picking another green object is $\frac{3}{8}$.

Step2: Calculate the combined probability

Using the multiplication rule for independent - dependent events (since the first pick affects the second pick), we multiply the two probabilities: $\frac{4}{9}\times\frac{3}{8}$.

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Answer:

$\frac{1}{6}$