Here is a question asked in a job interview at Qualcomm Inc.

An unfair coin with P(H) = 0.3 = 1-P(T) is tossed 10 times. Find the probability of getting even numbers of heads.

Electrical engineering majors are encouraged to try.

Eyes nepal. The way you think is absolutely right and you are almost there . But you completely ignoring  the number of toss. 

Mero sano dimag le nikalya answer chahi    0.47   ho.  I may be wrong.

let me explain how i came to this.

n is number of tries  = 10
r is chance of getting
Probablity of head in each toss P(H) = 0.3
Probablity of tais in each toss P(T) = 0.7

Probablity of getting 2 Heads  P (2H)  =  n C r  *  (0.3) power 2  * (0.7) power 8
                                                          =  10 C 2 * (0.3) power 2  * (0.7) power 8
                                                           =0.233

probablity of getting 4 Heads P(4H)=  10 C 4 *  (0.3) power 4 * (0.7) power 6
                                                      = 0.200

P(6H)=   10C6 *  (0.3) power 6  * (0.7) power 4
P (8H)=   10 C r8 *  (0.3) power 8  * (0.7) power 2
P(10H) = 10 C 10  *  (0.3) power 10  * (0.7) power 0

Now add everything = P(2H)+P(4H)+P(6H)+P(8H)+P(10H)
                                = 0.47

I may be wrong though. But this is what i came.

.

Hey smart allecs, just answer this ques. you will get a job,

see ya, 

If there are five apples, and you take away three, how many do you have?

  No quiero,

 I think you should also include P(0H) in the sum. Mathematically, 0 is also an even number. What do you think?

 Thanks!

Well. We dont know if 0 is odd or even and i dont think examiner will mind because what he looks for is the approach to solve the question.

Secondly, I think even we include 0 there would not be any visible change in the answer because  the term  (0.7) power 10 will make P(0H)  negligible.

  I don't want to discuss on the mathematical fact that 0 is an even number.
 You should include it although its effect is negligible here.
 It will not be negligible when the number of trials is small (say, n = 4) and P(T) is high (say 0.9).
 
 Am I right?

Well. Zero is not even or odd number. It is very debatable. So i didn't included in the equation. Some people say it as even, some say it as an odd number.

no_quiero,
lol...who says 0 is an odd number? Only those who have little knowledge of number theory. Most of us agree that zero "must" be even. Give me a single reason why zero can/should be odd? I can give you dozens of reasons as to why zero must be even.

As for the question, just use binomial theorem with the given p and even numbers as 0,2,4,6,8,10.

Exactly!

Who says 0 is not a even number?

No_quiero?

Ha ha ha............not Stephen Hawking!

Well. I never said zero is an odd number.  But i said it can't be classified as even or odd number. To explain this let me go back to the history about how ODD and EVEN was born.

In early days whatever people gets they used to share among each other. To make it simpler they created even or odd.

0 is not an odd number. However, many claim (including myself ) it isnt even number as well. There is still many controversies regarding zero.

Thing about a number being odd or even is if you can divide equally. Like if you have 8 apples you can divide among 2 people , four each.

However, Zero is nothing. So you can't distribute at all. So many people claim that zero can't be even or odd number. There is still big debate about zero being even number.

I for one don't call it an even number or odd number. So I can rightly justify my answer of probablity.


Mathematics is not often as straightforward as you say. Like anything divide by 2 is even because it leaves no remainder . There will always be time when you have to be analytical and  need to decipher yourself .

You may even say 0 divided by 0 is one   because anything divided by itself is one.  But it doesn't work like that. Zero is an anomaly and doesn't really exist. For any real number zero cannot be considered a number rather zero is an absence of number.

@3X.

Let me prove by another way why zero isnt even by following steps.

1. Lets start by assuming zero is even and it can be distributed equally among 2 people.

2. If something can be distributed equally. Then it must be finite number . because only finite  number are are measurable.  Because we can measure and know whether the number are equal or not. So 0 is a finite number.

3. We also know law of mathematics says finite number divided by finite number in mathematics should yield a finite number.  so say divide finite number 2 divide by finite number  0. should yield a finite number. However, here in division we get an infinite number.

Hence it proves our initial assumption was wrong and zero cannot be considered even. By considering even it may hold good for one law of mathematics but it  violates other law of mathematics. So zero is not really an even or odd number.

" Well. Zero is not even or odd number. It is very debatable. So i didn't included in the equation. Some people say it as even, some say it as an odd number."


Tell me who are these "some" who say 0 is odd.

oye curious about the answer.. didn't they give you the answer when you leave.. haha.. if you have then tell the answer..

Might be helpful:

http://en.wikipedia.org/wiki/Evenness_of_zero

http://mathforum.org/library/drmath/view/57188.html

These are not formal publications. So if someone has any journal paper related to evenness of zero, please post it.

But I am convinced on the conclusion that 0 is an even number.

@Bibas. Well all this thing has come while i solved the problem of probability. My point is you can't put zero in an even or odd number.r Thats why i didn't consider probability of zero in the question.


@3X  There are several complication while considering multiplication and division (in your case 0 divided by 2) of zero as per defining any set or rule in mathematics.  Hence division and multiplication of zero cannot be used to define evenness or oddness.

Let me give you one example,

Take an equation,

0=0    ( zero equals 0)

This equation can be re written as,

1²-1²=(1-1)<sup>2           (both side is again 0=0  as you may agree )

or, (1-1) (1+1) = (1-1) (1-1)


Now, taking out common term (1-1) from both side result,


1+1=1-1

2=0      Really?

You know this is not true. 

Let me tell you how this result came. The result came because of treating zero as any positve real natural number.  we treated term (1-1) divided by (1-1)     equals to 1.   Algebraically it may be true because x divided by x =1.
See how zero has made mockery of algebric equation that we have been doing all our life.

However, in reality  this term is zero divided by zero  and we we should not be  treating it as equal to 1.

Remember how we avoided zero in derivatives by taking limit tends to zero and not equal to zero.

My point is zero cannot be bound by any mathematical relation and define it in any set. We should leave zero as it is . It is neither negative nor positive, neither prime or neither non prime, neither odd nor even, anything divide by zero results infinity which is unmeasurable, any number multiplied by zero is zero .

So we know zero doesn't give one answer rather a set of answers for everything. So to say it is just divisible by 2 shouldn't make it count as even because zero gives similar result for everything. And even accepting the division, multiplication of zero for defining mathematical relations have resulted in many complication.

Some striking question about zero is,

How would you divide 0 which doesn't exist evenly among people ?

We know opposite of  1 is -1,  2 is -2. But what is opposite or negative number of 0.  Its like saying what is opposite of RED?

The fact is zero lies in borderline of everything.  negative and real positive number, set of odd and even numbers.

Lets put an analogy,
Remember days of physics when we read   how magnetic north and south pole points to nowhere in a borderline where earth north and south pole have similar effect. At that point we dont know whether we are closer to north pole or south pole because strength of both are same.

Same can be said about zero being in  a borderline of all the set of numbers.

I for one have never considered zero as an even.</sup> 

" Well. Zero is not even or odd number. It is very debatable. So i didn't included in the equation. Some people say it as even, some say it as an odd number."


I am still not satisfied. Tell me who are these "some" who say 0 is odd. You claimed this at the beginning. Now, if you are to back it up, give me the facts. Else, admit you made a mistake and apologize for misleading the Sajha visitors!!! :) (unless you are going to name ram, shyam, harke etc...)

" Well. Zero is not even or odd number. It is very debatable. So i didn't included in the equation. Some people say it as even, some say it as an odd number."


I am still not satisfied. Tell me who are these "some" who say 0 is odd. You claimed this at the beginning. Now, if you are to back it up, give me the facts. Else, admit you made a mistake and apologize for misleading the Sajha visitors!!! :) (unless you are going to name ram, shyam, harke etc...)

Bibas. Well many people don't admit it as even number. So with first look only other alternative is the odd number.  That's what used to be believed by very few people a history book of 0 " a natural history of zero". However, with time experts started to keep0 in even number and many experts kept  0 in neither odd nor even.  Do you know there are still many tribes which don't have number 0.

Whatever i wrote in that sentence was just plainly to make my point that I believe it is not an even number . Yeah I could have better said that some people may believe. I

If you go back before that the question that 3 X posted and I solved I believe 0 not as an even number. And I still haven't received any answer from 3 X about what is the right answer.

Again the same thing. Now, who are these "many people?" Initially it was "some" and now it is "many"
hehe...When you say many, it has to be more than 1, right? How many examples did you give? You can find zero being used as even in many textbooks and journals alike. When you go against the convention, you have to back it up...with some real good evidences.
 lol...after all this , you are expecting that people will consider your answer right? Do you think most people think the way you think? hehe.....just add the probability of 0 as well. That will solve your problem.


PS: I don't believe 2+2=4 This is bull****. I strongly believe 2+2=5. Am I wrong? hehe, it is about convention kid. We created the system of numbers. It was not there for us to just grab it. You can call  the "evens" as odds and vice versa. You can consider infinity to be a number and zero to be infinity. lol...its just that the landscape changes and we will have a different system, but we will prevail. So, learn to appreciate the importance of convention in mathematics.

bibas there is no point arguing with you. With people who may believe  i can't name tom, dick and harry. I have already told you to read a book called " a natural history of zero". This is the one of the reference book in our masters. If you want to you are free to read.

Regarding, zero not being an even number i have presented my points. I have also shown you have making zero as even present several mathematical complication. 

Secondly, I dont see any point arguing with you. You seem to pick a point and get stuck rather than trying to understand the whole idea put forwarded by me.  When i said " people may  believe zero as even or odd " meant that you are free to chose zero as per your convention because it will hold good in any event. I said this in regards to justify my answer of not chosing probablity of zero in the question of 3X. But if your idea is to irritate me then i should better not discuss with you.

Tell me when did i said zero as an infinity. Mate you seriously need some math tuition. I can continuely nag by copying same sentence you typed to me.

We had very intelligent question about probablity going on until you came and start to interrupt.