In an experiment, a fair coin is flipped, then a fair die is rolled, then second fair coins is flipped, ans outcomes are recorded. (outcome of a single trial of this experiment looks like H5T or T2T, meaning head was flipped then a 5 was rolled then a tail was flipped, or tail was flipped then a 2 was rolled then another tail was flipped.)

a)List sample space
b)let A be the event that odd number is rolled. find the probability of event A. Justify your answer
C) let B be the event exactly one T flipped and the number rolled is even. Find prob. event B. justify your answer.

Question

In an experiment, a fair coin is flipped, then a fair die is rolled, then second fair coins is flipped, ans outcomes are recorded. (outcome of a single trial of this experiment looks like H5T or T2T, meaning head was flipped then a 5 was rolled then a tail was flipped, or tail was flipped then a 2 was rolled then another tail was flipped.)

 a)List sample space
b)let A be the event that odd number is rolled. find the probability of event A. Justify your answer
C) let B be the event exactly one T flipped and the number rolled is even. Find prob. event B. justify your answer.

directrix · Answer

There are 24 possible outcomes. [2*6*2]

directrix · Answer

So, there are 24 elements in the sample space.

directrix · Answer

Tree Diagram and Half of the Members of the Sample Space

anonymous · Answer

T.T I hate Statistic... it is so difficult...
Thank you!

directrix · Answer

@Kokoa We are not finished. We have only just begun. The helpers ran off but are returning. :)

agent0smith · Answer

Once you get all the outcomes listed, b and c are easy - you can get them from the tree diagram. You can also get them without it.

directrix · Answer

a)List sample space
Half of it is on the attached file. @Kokoa  How about you following the pattern and listing the second 12 elements of the sample space. Just follow the limbs of the tree diagram. Once you get started, the pattern emerges.

directrix · Answer

@agent0smith 
>>Once you get all the outcomes listed, b and c are easy - you can get them from the tree diagram. You can also get them without it.

This is not logic, is it?

agent0smith · Answer

Eh? Not sure what you mean. You can get b and c w/o a tree diagram.

directrix · Answer

How did you calculate 1/2?

The explanation of how to get 1/2 and the commentary that it is easy to do are not the same thing.

agent0smith · Answer

^ The chance of an odd number from the die is 50% (three odd numbers, six possible outcomes), and is independent of the coin outcomes. 

chance of getting one tail is 50% (two outcomes TH and HT, four possible TH, TT, HT HH) and the chance of an even number is also 50%, so multiply them together.

agent0smith · Answer

^and again, an even number and exactly one T are independent events.

agent0smith · Answer

"How did you calculate 1/2?

The explanation of how to get 1/2 and the commentary that it is easy to do are not the same thing."

I think you may have been confusing me with qweqwe123123123123111 ?

directrix · Answer

I looked at the tree diagram and saw 6 odd numbers on the first half and knew that there would be the same 6 on the second half of the tree.

So that makes 12 of the 24 outcomes have odd numbers. Probability is the number of desired outcomes divided by the number of possible outcomes. So, that is 12/24 = 1/2 as the probability for part b. 

That is what I mean by an explanation. Or, maybe you already said that while I was drawing that tree. :)

directrix · Answer

>> @qweqwe123123123123111  Quite possible because I was reading the posts and not looking at the author. My apology to you @agent0smith

directrix · Answer

Let me look at part c again.

directrix · Answer

@qweqwe123123123123111  Come over here in this thread and post. We are finished with the 3rd child is a girl post. (Please)

directrix · Answer

For part C, 
T1H, T3H, T5H, H1T, H3T, H5T

6/24 = 1/4 --> the aforementioned 25%

directrix · Answer

@Kokoa   You have to help on this. So, do you know how to finish the sample space?

agent0smith · Answer

For part c, the order of the events doesn't matter - it only matters that you get an even number (3/6) and exactly one T (2/4).

You can get the same results from a tree diagram, but since the events are independent, it's not necessary (like it kinda is with dependent events)

anonymous · Answer

Yes! Thank You!!! Thank you!   
All of you are amazing!

directrix · Answer

We enjoy working together (and debating) on these types of problems @Kokoa

agent0smith · Answer

A tree diagram can still help though, to confirm an answer.

directrix · Answer

Somebody over in the "third girl" thread said a tree diagram for this problem would be useful. :)  I think it helped @Kokoa and I like the tree diagrams so it's all good.

anonymous · Answer

- " Come over here in this thread and post"

Okay...stand by...  :-)

agent0smith · Answer

I said it :P but that's because this question ask for a sample space, and a tree diagram helps to list them all w/o forgetting some.

directrix · Answer

I agree. But, it is also easy to get mesmerized when drawing all those limbs and then reading off the sample space items.

agent0smith · Answer

Tree diagrams are almost a necessity when events are dependent, though, since in those cases, the order of the events does matter.

directrix · Answer

@Kokoa is playing Chuck-A-Luck now in a new post. It's a cool game. Read about it here: http://homepage.ntlworld.com/dice-play/Games/ChuckALuck.htm