A coin is tossed three times: The probability of zero heads is 1/8 and the probability of zero tails

slijmigrd 2022-07-07 Answered
A coin is tossed three times: The probability of zero heads is 1/8 and the probability of zero tails is 1/8.

And my question is: What is the probability that all three tosses result in the same outcome?

So, if P(zero heads)= 1/8 , then that should be the same of p(all tails)?

If so, we could use the Addition Rule which is P ( A B ) = P ( A ) + P ( B )

where A and B are disjoint events, i.e. A A B = , A is the event of tossing all heads and B is the event of tossing all tails.

I'm not sure how to continue after that... would the complement be used?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Jayvion Tyler
Answered 2022-07-08 Author has 23 answers
Let A be the desired event. Then
P ( A ) = P ( H H H ) + P ( T T T ) = 1 8 + 1 8 = 1 4 .
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-07-09
A game is played by rolling a six sided die which has four red faces and two blue faces. One turn consists of throwing the die repeatedly until a blue face is on top or the die has been thrown 4 times
Adnan and Beryl each have one turn. Find the probability that Adnan throws the die more turns than Beryl
I tried : Adnan throws two times and Beryl throws once = 2 3 x 1 3
Adnan throws three times and Beryl throws once = 4 9 x 1 2
Adnan throws three times and Beryl throws twice = 4 9 x 2 3
Adnan throws four times and Beryl throws once = 8 27 x 1 2
Adnan throws four times and Beryl throws twice = 8 27 x 2 3
Adnan throws four times and Beryl throws three times = 8 27 x 4 9
The answer says 0.365
asked 2022-06-15
If you roll 5 dices and get three of the same dices, is it better to leave one and roll one or roll two dices?
My friend is saying that it is better to leave one and roll another, since that will give you a full house in 1/6 probability.
However, I thought it is better to roll both different dices since that will give 5/36 full house and 1/36 yahtzee.
Am I wrong in thinking that it is always better to roll two dices since yahtzee scores more than full house given that both full house and yahtzee are open?
asked 2022-07-15
What is the difference between events that are mutually exclusive and those that are not mutually exclusive?
asked 2022-05-09
Getting 2 or 5 in two throws should be P ( 2 ) + P ( 5 ). P ( 2 ) = 1 / 6 , P ( 5 ) = 1 / 6 so the combined so it should be 1/3.
I tried to visualize but not able to do so correctly.
11,12,13,14,15,16, 21,22,23,24,25,26,31,32, ....6,6
total of 36 possibilities.
12,15,21,22,23,24,25,26,31,35,42,45,51,52,53,54,55,56,61,65
out of which 20 possibilities, so the probability should be 20/36 which is not 1/3.
Where am I going wrong?
asked 2022-06-16
I'm trying to prep myself for entrance exams and struggle with the following problem:
Mr. X uses two buses daily on his journey to work. Bus A departs 6.00 and Mr. X always catches that. The journey time follows normal distribution (24,42). Bus B departs at 6.20, 6.30 and 6.40, journey time following normal distribution (20,52), independent of bus A. We assume the transfer from bus A to B won't take time and Mr. X always takes the first bus B available. Calculate probability for Mr. X being at work before 6.55.
So I am aware that the sum of two normal distribution variables follows also normal distribution, but don't know how two proceed with the given departure times of bus B (6.20, 6.30, 6.40) as clearly I can't just calculate the probability of A+B being under 55 minutes.. Any tips how to start with this?
asked 2022-04-07
There's an 80% probability of a certain outcome, we get some new information that means that outcome is 4 times more likely to occur.
What's the new probability as a percentage and how do you work it out?
As I remember it the question was posed like so:

Suppose there's a student, Tom W, if you were asked to estimate the probability that Tom is a student of computer science. Without any other information you would only have the base rate to go by (percentage of total students enrolled on computer science) suppose this base rate is 80%.
Then you are given a description of Tom W's personality, suppose from this description you estimate that Tom W is 4 times more likely to be enrolled on computer science.
What is the new probability that Tom W is enrolled on computer science.

The answer given in the book is 94.1% but I couldn't work out how to calculate it!
Another example in the book is with a base rate of 3%, 4 times more likely than this is stated as 11%.
asked 2022-05-30
Having been reprimanded for posting a question on the wrong site, I hope I'm not transgressing this time. In the addition rule for non mutually exclusive events P ( A B ) = P ( A ) + P ( B ) P ( A B ), while P ( A B ) can be determined by observation, why cannot it always be calculated from P ( A ) P ( B )?

Example: A lottery box contains 50 lottery tickets numbered 1 to 50. If a lottery ticket is drawn at random, what is the probability that the number drawn is a multiple of 3 or 5? P ( X Y ) = P ( X ) + P ( Y ) P ( X Y ) Therefore,
P ( X U Y ) = 8 / 25 + 1 / 5 3 / 50 = ( 16 + 10 3 ) / 50
= 23 / 50
But using P ( X Y ) = P ( X ) P ( Y ) = 8 / 25 1 / 5 = 8 / ( 25 5 ) = 8 / 125 which is NOT 3/50?
There are situations where P ( X Y ) = P ( X ) x P ( Y ) works perfectly, but not in others.

New questions

i'm seeking out thoughts for a 15-hour mathematical enrichment course in a chinese language high faculty. What (pretty) simple concern would you advocate as a subject for any such course?
historical past/issues:
My students are generally pretty good at math, but many of them have no longer been uncovered to rigorous or summary mathematical reasoning. an amazing topic would be one that could not be impossibly hard for students who have by no means written or study proofs in English.
i have taught this magnificence three times earlier than. (a part of the purpose that i'm posting that is that i have used up all my thoughts!) the primary semester I taught an introductory range theory elegance (which meandered its way toward a proof of quadratic reciprocity, though I think this become in the end too advanced/abstract for some of the students). the second one semester I taught fundamental graph idea and packages (with a focal point on planarity and coloring). The 1/3 semester I taught a class at the Rubik's dice.
the students' math backgrounds are pretty numerous: a number of them take part in contest math competitions, and so are familiar with IMO-fashion techniques, however many aren't. a number of them may additionally realize some calculus, however I cannot assume it. all of them are superb at what in the united states is on occasion termed "pre-calculus": trigonometry, conic sections, systems of linear equations (though, shockingly, no matrices), and the like. They realize what a binomial coefficient is.
So, any ideas? preferably, i'd like to find some thing a bit "sexy" (like the Rubik's cube) -- tries to encourage wide variety theory through cryptography seemed to fall on deaf ears, however being capable of "see" institution idea on the cube became pretty popular.
(Responses specifically welcome from folks who grew up in the percent -- any mathematical subjects you desire were protected within the excessive college curriculum?)