Question

suppose 7 blue and 3 green 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(\text{green} | \text{blue}) =? )

b) what is the probability of obtaining a final outcome with at least one green object?

Explanation:

Step1: Find conditional probability \(P(Green|Blue)\)

Conditional probability \(P(Green|Blue)\) is directly given in the tree - diagram. When the first object is blue, the probability of the second object being green is \(\frac{3}{9}=\frac{1}{3}\)

Step2: Find probability of at least one green object

The probability of no green objects (i.e., two blue objects) is \(P(Blue\cap Blue)=\frac{7}{10}\times\frac{6}{9}=\frac{7\times6}{10\times9}=\frac{42}{90}=\frac{7}{15}\)
The probability of at least one green object is \(P = 1 - P(Blue\cap Blue)\)

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Answer:

a) \(\frac{1}{3}\)
b) \(\frac{8}{15}\)