Statistics help, probability tree diagram

In summary, the conversation discusses a gameshow with 10 contestants, 6 of whom are female. Each round, one contestant is eliminated and all have an equal chance of progressing. The first question asks to show that the probability of the first two eliminated contestants being male is 2/15. The second question asks for the probability that more females than males will be eliminated in the first three rounds. The third question asks for the probability that, given the first elimination is male, the next two eliminations will be female. The conversation also includes a request for help with a tree diagram, in which the branches should represent 'female eliminated' and 'male eliminated'. The expert suggests simplifying the branches to make the diagram clearer.
  • #1
tweety1234
112
0

Homework Statement



At the start of a gameshow there are 10 contestants of which 6 are female. In each round of
the game, one contestant is eliminated. All of the contestants have the same chance of
progressing to the next round each time.
(a) Show that the probability that the first two contestants to be eliminated are
both male is 2/15

(b) Find the probability that more females than males are eliminated in the first three
rounds of the game.

(c) Given that the first contestant to be eliminated is male, find the probability that the next
two contestants to be eliminated are both female.

Please can someone help me with this question, I am really stuck. I have drawn a tree diagram but I don't think it is correct, as it does not give the right answer. Can someone have a look at it and show me were I have gone wrong? Or show me what the tree diagram should look like.

from my tree diagram I get the answer for questions 'c'

([tex] \frac{6}{10} \times \frac{5}{9} \times \frac{4}{8} [/tex] )+ ( [tex] \frac{6}{10} \times \frac{4}{9} \times \frac{5}{8} [/tex]) + ([tex] \frac{6}{10} \times \frac{5}{9} \times \frac{4}{8} [/tex] ) + ([tex]\frac{4}{10} \times \frac{6}{9} \times \frac{5}{8} [/tex] )




thank you!



btw- 'E'- stands for elimnated
NE- stands for not elminated.


http://www.mathhelpforum.com/math-help/attachments/basic-statistics-probability/10795d1238940269-tree-diagram-probability-untitled.jpg [Broken]
 
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  • #2
You seem to be summing up too many branches. Look back at your tree: instead of saying 'E and NE' it should be 'female eliminated and male eliminated' (to make things clearer). Then, which branch is the one that gives the probability of 'given the first elimination is male, what is the probability the second two are both female'?
 
  • #3
cristo said:
You seem to be summing up too many branches. Look back at your tree: instead of saying 'E and NE' it should be 'female eliminated and male eliminated' (to make things clearer). Then, which branch is the one that gives the probability of 'given the first elimination is male, what is the probability the second two are both female'?

But since its 3 rounds, than should it not be 3 branches? I will re-draw my diagram and post it up.

thank you.
 

1. What is a probability tree diagram?

A probability tree diagram is a graphical representation of all possible outcomes in a probabilistic scenario. It is used to help calculate the probability of a certain event occurring by breaking down the event into smaller, more manageable outcomes. The diagram consists of branches and nodes, with each branch representing a different outcome and each node representing a decision point.

2. How do I create a probability tree diagram?

To create a probability tree diagram, you first need to identify the different possible outcomes of the event and assign probabilities to each outcome. Then, draw a line representing each outcome from a starting point. At each branch, label the probability of that outcome. Continue branching until you have reached all possible outcomes. Finally, calculate the probabilities of the final outcomes by multiplying the probabilities along each branch.

3. When should I use a probability tree diagram?

A probability tree diagram should be used when dealing with multiple events or decisions that can affect the outcome of a particular event. It is particularly useful in calculating conditional probabilities, where the probability of one event is dependent on the occurrence of another event. It is also helpful when there are a large number of outcomes and it is difficult to calculate the probabilities using other methods.

4. Can I use a probability tree diagram for non-numerical data?

Yes, a probability tree diagram can be used for non-numerical data. In such cases, the probabilities assigned to each outcome would be based on frequency or likelihood rather than numerical values. For example, if the outcomes are "red," "blue," and "green," the probabilities could be expressed as a percentage or a fraction.

5. How can I interpret the results of a probability tree diagram?

The results of a probability tree diagram can be interpreted as the likelihood of a particular outcome or event occurring. The closer the calculated probability is to 1, the more likely the event is to occur. On the other hand, a probability close to 0 indicates a low likelihood of the event occurring. It is important to note that the probabilities calculated from a probability tree diagram are based on assumptions and may not accurately reflect real-life situations.

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