*** Problems

krassi_holmz · 2006-04-23 04:55:21

28.

Jai Ganesh · 2006-04-23 16:09:19

Excellent, krassi_holmz! Keep up the good work!

Jai Ganesh · 2006-04-24 17:07:06

***29. Out of 40 students, 25 are boys, 16 are married, 10 are married boys. What is the probability that a chosen student would be an unmarried girl?

Jai Ganesh · 2006-05-02 03:06:04

***30. If x,y, and z be respectively the sums of p, q, and r terms of an Arithmetic Progression, prove that

Jai Ganesh · 2006-06-07 02:26:04

***31. Two numbers are selected at random from 1,2,3,4,....100 and are multiplied. Find the probability of the product being a multiple of 3.

***32. A and B are two independent events. The probability that both A and B occur is 1/6 and that of neither of them occuring is 1/3. Find the probability of occurence of A.

Ninja 101 · 2006-06-12 00:34:34

Annoyed statement:
I can never read that writing like in ***30
and what's more I told you.

lightning · 2007-03-24 10:07:13

they are 10 boy marred too each other?

Devantè · 2007-03-24 10:28:18

Firstly, don't post in a 9-month-old thread unless you have something to contribute...I think even you know that 10 boys are not married to each other.

lightning · 2007-03-24 10:31:31

this is 9 months old? i no that but it's a puzzle it's sopost to be tricky!

Eeyore · 2007-04-24 05:09:28

ganesh wrote:

***32. A and B are two independent events. The probability that both A and B occur is 1/6 and that of neither of them occuring is 1/3. Find the probability of occurence of A.

Sorry, not enough information to find a unique solution.

I found that P(A) is not equal to P(B). And, since A and B are interchanged "without loss of generality," a.k.a. WOLOG,
then it seems there are two possibilities for P(A).

Stanley_Marsh · 2007-04-27 05:37:33

To 31
there are 33 numbers which are the multiple of 3 , then the probability of chosing one from 1-100 will be 33/100 , if u chose two number which are not the multiple of 3 , then the probability is (67/100)^2 , then the probability we want is 1- (67/100)^2

To 32 ,
P(A)=x , P(B)=y
xy= 1/6 , (1-x)(1-y)=1/3
y=5/7 ,x= 7/30

Last edited by Stanley_Marsh (2007-04-27 05:42:58)

mathsyperson · 2007-04-27 07:18:22

Or perhaps x=5/7, y=7/30. We don't know, and that's the point Eeyore was making.
Wologs are cute.

Stanley_Marsh · 2007-04-27 10:35:40

I check that
P(A on , B off) + P(B on , A off ) + P(A on ,B on ) +P(A off ,B off ) =1

Jai Ganesh · 2007-09-30 01:32:54

***33. A Pythagorean triple is a set of three numbers such that the sum of squares of the first two numbers is equal to the square of the third. For example, (3,4,5) is a Pythagorean triple. These formthe lengths of the three sides of a right angled triangle.

Prove that there are an infinite number of primitve Pythagorean triples ( The set (6,8,10) is a Pythagorean triple but not a primitve Pythagorean triple because it is of the form(3n,4n,5n) where n=2 and (3,4,5) is a Pythagorean triple. For example,another primitve Pythagorean triple is(5,12,13)).

Jai Ganesh · 2007-10-01 19:16:49

***34. Prove that a rhombus is a cyclic quadrilateral if and only if it is a square.

***35. Prove that a parallelogram is a cyclic quadrilateral if and only if it is rectangle.

Jai Ganesh · 2007-10-14 02:05:33

***36. In a get-together, every person present shakes hand with every other person once. If there are 91 handshakes in all, how many persons attended the party?

pi man · 2007-10-14 11:45:25

Last edited by pi man (2007-10-14 11:47:56)

JaneFairfax · 2007-10-14 13:19:52

Jai Ganesh · 2007-10-15 00:08:45

Outstanding, pi man and Jane Fairfax!!!

Jai Ganesh · 2007-10-19 02:24:03

37. A vendor has a pair of weighing scales and four weights, the total of all the four weights being 40 kilograms. With the help of any or multiple of these four weights alone and only one wighing on the scale, he can weigh any integral value of weight from 1 to 40 kilograms, both inclusive. How many do these four weights measure?

Jai Ganesh · 2007-10-30 03:33:41

38. Can you give a list of 1,000 consecutive non-primes?

Jai Ganesh · 2007-10-31 03:22:47

39. How many prime numbers approximately lie between 1 and 1000?

40. What do 1296 and 625 have in common?

JaneFairfax · 2007-10-31 03:31:58

mathsyperson · 2007-10-31 04:12:31

JaneFairfax · 2007-10-31 04:23:47

ganesh wrote:

Non primes are natural numbers that are not prime, also known as composite numbers.

No, not all natural numbers that are not prime are composite numbers!

A composite number is a number that is a product of two or more prime numbers. The number 1 is not a composite number. However, the number 1 is a natural number that is not prime!

So, do you want composite numbers (which will exclude 1), or do you want non-prime natural numbers (which will include 1)?

Last edited by JaneFairfax (2007-10-31 05:34:07)

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