Question

suppose 7 blue and 5 yellow 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 ( c =? )
c) what is the value of the branch probability ( f =? )

Explanation:

Step1: Calculate the probability of selecting blue first (a)

The total number of objects initially is \(7 + 5=12\). The probability of selecting a blue object first is the number of blue objects divided by the total number of objects. So, \(a=\frac{7}{12}\).

Step2: Calculate the probability of selecting blue second after blue first (c)

After one blue object is selected (without replacement), the number of blue objects left is \(7 - 1 = 6\) and the total number of objects left is \(12- 1=11\). So, \(c=\frac{6}{11}\).

Step3: Calculate the probability of selecting yellow second after yellow first (f)

After one yellow object is selected (without replacement), the number of yellow objects left is \(5 - 1=4\) and the total number of objects left is \(12 - 1 = 11\). So, \(f=\frac{4}{11}\).

Answer:

a) \(\frac{7}{12}\)
b) \(\frac{6}{11}\)
c) \(\frac{4}{11}\)