Question

suppose 5 red and 6 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, but the branch probabilities are missing.
note: for all questions below, please enter your answers in fraction form.
a) what is the value of the branch probability ( a = )?
b) what is the value of the branch probability ( d = )?
c) what is the value of the branch probability ( e = )?

Explanation:

Step1: Calculate the total number of objects

The total number of objects initially is \(5 + 6=11\).

Step2: Find the value of \(a\)

The probability of picking a red object first (\(a\)) is the number of red objects divided by the total number of objects. So \(a=\frac{5}{11}\).

Step3: After picking a red object first, find the value of \(d\)

After picking one red object, there are \(11 - 1 = 10\) objects left, with \(6\) green objects. So \(d=\frac{6}{10}=\frac{3}{5}\).

Step4: After picking a green object first, find the value of \(e\)

The probability of picking a green object first (\(b\)) is \(\frac{6}{11}\). After picking one green object, there are \(11- 1=10\) objects left, with \(5\) red objects. So \(e = \frac{5}{10}=\frac{1}{2}\).

Answer:

a) \(\frac{5}{11}\)
b) \(\frac{3}{5}\)
c) \(\frac{1}{2}\)