Bayes' Theorem: Probability of 8 Heads in 10 Tosses?

[Tajeshwar]

Homework Statement

Suppose I have a bent coin with a 60% probability of coming up heads. I throw the coin ten times and it comes up heads 8 times.

What is the value of the “likelihood” term in Bayes’ Theorem -- the conditional probability of the data given the parameter.

Homework Equations

The Attempt at a Solution

My attempt was 8 heads in a row should be (.6)^8... That comes to .0167. However, that is not one of the choices.

#4 almost matches, but there is a difference in the decimal.

The answer choices are:

0.120932
0.122885
0.168835
0.043945
[/B]

 

[Orodruin]

The question is not asking you for the probability for the coin to comu up heads 8 times in a row. It is asking you for the probability for it to come up heas 8 times in 10 tosses.

 

[Ray Vickson]

Homework Statement

Suppose I have a bent coin with a 60% probability of coming up heads. I throw the coin ten times and it comes up heads 8 times.

What is the value of the “likelihood” term in Bayes’ Theorem -- the conditional probability of the data given the parameter.

Homework Equations

The Attempt at a Solution

My attempt was 8 heads in a row should be (.6)^8... That comes to .0167. However, that is not one of the choices.

#4 almost matches, but there is a difference in the decimal.

The answer choices are:

0.120932
0.122885
0.168835
0.043945[/B]

(1) Please stop using bold font; it looks like you are yelling at us.
(2) There are many "sample points" in the event "E = {8 heads in 10 tosses}"; for example, three possible outcomes in E would be HHHHHHHHTT or TTHHHHHHHH or THTHHHHHHH, and there are several others as well. To get the probability of 8 heads you need to compute each such probability and then add them all up! There is a very familiar probability distribution associated with such problems, and you can very likely get a lot of relevant information by reading your textbook or course notes. Google is your friend as well.

 

[Tajeshwar]

(1) Please stop using bold font; it looks like you are yelling at us.
(2) There are many "sample points" in the event "E = {8 heads in 10 tosses}"; for example, three possible outcomes in E would be HHHHHHHHTT or TTHHHHHHHH or THTHHHHHHH, and there are several others as well. To get the probability of 8 heads you need to compute each such probability and then add them all up! There is a very familiar probability distribution associated with such problems, and you can very likely get a lot of relevant information by reading your textbook or course notes. Google is your friend as well.

Sorry about the bold font. I did not realize that was offensive or I was even doing it. Thank you for pointing it out.

I also appreciate your guidance on this question.

I tried the binomial theorem for exactly 8 heads and that has led me to one of the choices. So that is what they must be asking. Let me see if it works out.

I think the general level of people on this forum is quite advanced and that is why my questions may seem a little too simplistic. Hopefully, I will keep learning and get there slowly.

 

[Tajeshwar]

The question is not asking you for the probability for the coin to comu up heads 8 times in a row. It is asking you for the probability for it to come up heas 8 times in 10 tosses.

Yes thank you. That helped. Appreciate your guidance.