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.

Well I'm not engineering major but here's my mouth calculated answer

the 1-P(T) = 3 for the 10 toss

P(getting even number's of heads) = 0.1

let me know if I got it.

Eyes Nepal,

Good try!

But when you say 1-P(T) = 3 for 10 toss, you will be instantly asked to leave the interview.

Forget about engineering majors. Such answer is generally not expected even from a lower secondary level student.

Anyway, you tried it. That is great!!!!!!!!

Here you go 3X

if 1-P(T) = .3

P(H)= .3

P(even numbers of head)= P(2H)+P(4H)+........+P(10)H

                                    =.09+.0081+.......

                                    = Approx    .1

I won't be surprised if some dhoti have asked such question. and as per your idea if they asked people to leave for such answers they will be end up with hiring crazy mathematicians only. The HR don't look for right answers instead they will look for how your attitude and your potential effort to answer those question.

By the way did anyone get call from quallcomm for the summer Intern.

 

EyesNepal,

Its great that you are trying. Keep on trying. I hope you will be able to get the correct answer.

When one is an MBA graduate, then your reasoning on hiring might be right, I don't know. Attitude counts, but I think it is the secondary factor against your reasoning power in case of engineering jobs.

This question was asked to an Indian graduate student (my senior) by a white-skinned engineer of Qualcomm. He is in Qualcomm now. I am just sharing the question as it is the time to apply for internships.

Cheers!

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>