HELP! Easy Probability need by tommorrow!!

: If you toss a coin 7 times whats the probability of getting exactly 3
: heads? It seems so easy but i have gotten a bunch of different
: answers that all seem right. Help please ASAPWho are you and why do you need a rush answer to this question? If this is a homework assignment or take-home test, and you are not allowed to get anyone to do it for you, stop now. Reading any further is cheating.If you are a lost teacher, or a college/high school student and this is NOT being graded, here’s the answer:Note — this is a classic problem, and this is, I promise you, the exact answer; other varying answers may be miscalculations, or people who have not studied probability trying to make it up for themselves.This is what is called a *Bernouilli Trial*. Look up this term in any introductory probability bookFirst, think about lining up seven identical coins with three of them showing heads and four showing tails. Notice that there are a LOT of different ways you can do this: HHHTTTT, HHTHTTT, HHTTHTT, … TTHHTHT, … TTTHHHYou need to count how many ways of lining up three heads and four tails. A list is possible but very very long. So we use what are called *combinations* (look up again) We need to choose three places out of seven to put an H (and then the rest are T) so we need what is called *7 choose 3*, written C(7,3) OR 7C3 OR large parentheses with a 7 above a 3 but NO fraction bar.Fact: 7C3 = (7!)/((7-3)! x 3!) = (7!)/(4! x 3!) = (7x6x5)/(3x2x1) = 35The exclamation points are read *factorial* (look up) 7 factorial = 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = number of different ways 7 distinct objects or people can be put in order.OK, back to problem. You want three H. You know that the probability of H on any one throw of a fair coin is 1/2. So the probability of H on three throws in a row is 1/2 x 1/2 x 1/2 or (1/2) ^3 = 1/8 (^ implies exponent — think of it as an arrow telling you to write the three up high, as third power) Now, having exactly three H ALSO implies you have four T (no choice). Probability of having four T is 1/2 x 1/2 x 1/2 x 1/2 = (1/2) ^4 = 1/16So the probability of getting exactly three H out of seven throws of a fair coin is35 [ways of ordering the answer] X (1/2)^3 [probability of 3H] X (1/2) ^4 [probability of remaining 4 being T]= 35 X 1/8 X 1/16 = 35/128Decimal equivalent is clearly a little more than 1/4 or .25, maybe .26

The person who posted this question, as well as a previous question about geometry, is not a responsible web user/student.He/she (calls self Sunny here), email [email protected](1) demands immediate answers (2) does not acknowledge answers once you provide them (3) is using this help for a course he/she is taking (4) does not tell you that this is course work (5) gave a very offensive, personally insulting reply when I asked privately by email if this was course workWhen a student asks for immediate answers without admitting that it is class work, the suspicion arises that this is cheating for graded homework. It is only a suspicion, not a proof, of course, so I tried to check by private email. I have politely asked this person twice what the situation is, and warned of the potential problem in my answers, in order to clarify what amount and type of help is reasonable. The reply was personally insulting and offensive.This person is also one who feels quite comfortable making immediate and forceful demands on total strangers, but gets upset if you give a straightforward question back.I would suggest that any other math tutors who read the web avoid answering any more posts of this type from this source.

: The person who posted this question, as well as a previous question
: about geometry, is not a responsible web user/student.: He/she (calls self Sunny here), email [email protected]: (1) demands immediate answers (2) does not acknowledge answers once
: you provide them (3) is using this help for a course he/she is
: taking (4) does not tell you that this is course work (5) gave a
: very offensive, personally insulting reply when I asked privately
: by email if this was course work: When a student asks for immediate answers without admitting that it
: is class work, the suspicion arises that this is cheating for
: graded homework. It is only a suspicion, not a proof, of course,
: so I tried to check by private email. I have politely asked this
: person twice what the situation is, and warned of the potential
: problem in my answers, in order to clarify what amount and type of
: help is reasonable. The reply was personally insulting and
: offensive.: This person is also one who feels quite comfortable making immediate
: and forceful demands on total strangers, but gets upset if you
: give a straightforward question back.: I would suggest that any other math tutors who read the web avoid
: answering any more posts of this type from this source.Victoria,Good for you - I agree with your response and was quiet surprised that you didn’t recieve a thankyou last time from this person. The amount of effort you put in to the geometry problem was exceptional and taken for granted.I couldn’t believe that this person had the nerve to ask for more!!!!!! You effort is needed by the others that you have helped and that really are looking to understand. Bravo to you!Terri

Oh Victoria, you deserve MANY MANY MANY thanks for helping to infuse life into this once dead board!!!!! Don’t take thoughtless or ungrateful people to heart. Know that many others are probably benefiting from your answers to them.I read each of your posts with relish! I marvel at the time you are willing to spend writing such detailed and practical explanations. I wish you could be my son’s math teacher!!!!I just hope we don’t burn you out. I would really hate to see this board go dead again.