SOLUTION: Hello there, I need your help on probability-tree diagram. I'm very thankful if anyone could help me on this. Thanks! In a class, the probability that a student wears a watch is

Question 596322: Hello there, I need your help on probability-tree diagram. I'm very thankful if anyone could help me on this. Thanks!
In a class, the probability that a student wears a watch is 0.8. Three students are randomly selected from the class.
(A) Draw a tree diagram showing all posible outcomes and their probabilities.
(B) What is the probabilty that
(i) all three students wear a watch
(ii) only te first three student wears a watch
(iii) only one student does not wear a watch
(iv) none of the three student wears a watch
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a class, the probability that a student wears a watch is 0.8. Three students are randomly selected from the class.
(A) Draw a tree diagram showing all posible outcomes and their probabilities.
-----
Note: You did not post the number of students in the class. You
only indecated that 3 were selected.
---
Let the Root column be A ; B ; C ; etc. (depending on number in the class = n).
---
To the right of the Root column put the 1st Branch column
which has "watch" ; "no watch" to the right of each Root
element. That column should have 2n elements in it.
---------------------------------------
Next to each "watch" put 0.8
Next to each "no watch" put 0.2
=======================================
(B) What is the probabilty that
(i) all three students wear a watch: nC3*0.8^3*0.2^(n-3)
--------------------
(ii) only the first three student wears a watch: 0.8^3*0.2^(n-3)
------------------------
(iii) only one student does not wear a watch: nC1(0.2)*0.8^(n-1)
-------------------------------------
(iv) none of the three student wears a watch: nC3(0.2)^3*0.8^(n-3)
====================================
Cheers,
Stan H.
====================================

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