0
Integers a b c and d not necessarily distinct are chosen independently and at random from 0 to 2007 inclusive What is the probability that ad-bc is even?
10/16 = .625
Analysis:
a and d will be odd if and only if both are odd. Therefor, ad will be odd 1/4 the time.
The same goes for bc. It will be odd 1/4 off the time.
ad-bc is even if and only if both ad and bc are either odd or even.
It's easiest to solve it from here with a table:
ad bc ad-bc prob
even even even 3/4*3/4 = 9/16
even odd odd 3/4*1/4 = 3/16
odd even odd 1/4*3/4 = 3/16
odd odd even 1/4*1/4 = 1/16
So, ad-bc will be even 9/16+1/16 = 10/16 of the time.
What else can I help you with?
What is the probability of a square number?
In the set of the first n integers, the number of a square number is approximately sqrt(n). So the probability of a square number is sqrt(n)/n = 1/sqrt(n). As n becomes larger this probability tends towards 0.
An integer between 1 and 100 Find probability of perfect square if all integers between 10 and 80 as twice as the rest?
15/100=0.15
What is the probability that a randomly chosen number is not divisible by 2 3 or 6?
AnswerThe probability that a randomly chosen [counting] number is not divisible by 2 is (1-1/2) or 0.5. One out of two numbers is divisible by two, so 1-1/2 are not divisible by two.The probability that a randomly chosen [counting] number is not divisible by 3 is (1-1/3) = 2/3.Similarly, the probability that a randomly chosen [counting] number is not divisible by N is (1-1/N).The probability that a random number is not divisible by any of 2, 3 or 6 can be reduced to whether it is divisible by 2 or 3 (since any number divisible by 6 can definitely be divided by both and so it is irrelevant). This probability depends on the range of numbers available. For example, if the range is all whole numbers from 0 to 10 inclusive, the probability is 3/11, because only the integers 1, 5, and 7 in this range are not divisible by 2, 3, or 6. If the range is shortened, say just from 0 to 1, the probability is 1/2.Usually questions of this sort invite you to contemplate what happens as the sampling range gets bigger and bigger. For a very large range (consisting of all integers between two values), about half the numbers are divisible by two and half are not. Of those that are not, only about one third are divisible by 3; the other two-thirds are not. That leaves 2/3 * 1/2 = 1/3 of them all. As already remarked, a number not divisible by two and not divisible by three cannot be divisible by six, so we're done: the limiting probability equals 1/3. (This argument can be made rigorous by showing that the probability differs from 1/3 by an amount that is bounded by the reciprocal of the length of the range from which you are sampling. As the length grows arbitrarily large, its reciprocal goes to zero.)This is an example of the use of the inclusion-exclusion formula, which relates the probabilities of four events A, B, (AandB), and (AorB). It goes like this:P(AorB) = P(A) + P(B) - P(AandB)In this example, A is the event "divisible by 2", and B is the event "divisible by 3".
How may two digit-numbers contain the digit 4?
18 positive integers and 36 integers (negative and positive)
What is the probability that a random selected poker hand contains exactly 3 aces given that it contains at least 2 aces?
To calculate the probability of a random selected poker hand containing exactly 3 aces given that it contains at least 2 aces, we first need to determine the total number of ways to choose a poker hand with at least 2 aces. This can be done by considering the different combinations of choosing 2, 3, or 4 aces from the 4 available in a standard deck of 52 cards. Once we have the total number of ways to choose at least 2 aces, we then calculate the number of ways to choose exactly 3 aces from the selected hand. Finally, we divide the number of ways to choose exactly 3 aces by the total number of ways to choose at least 2 aces to obtain the probability.
How many positive integers between 1000 and 9999 inclusive a are divisible by 9?
There are 1,000 positive integers between 1,000 and 9,999, inclusive, that are divisible by nine.
Sum the integers from 1 to 100?
The sum of the integers from 1 to 100 inclusive is 5,050.
What is the sum from 1000 positive integers to 1100?
The sum of the positive integers from 1,000 to 1,100 inclusive is: 106,050
What is the sum of all integers from 1 to 20?
The sum of all integers from 1 to 20 inclusive is 210.
How many integers are there between -11 and 12?
There are 22 integers between them.
How many odd integers are there from 17 to 59 inclusive?
22.
What is the sum of the even integers from 2 to 100 inclusive?
2550
How many integers are between 0-10 inclusive?
10
Is the set of integers between 1 and 100 inclusive?
To be pedantic, it is not.
How many integers between 13 and 19 inclusive?
7
What are the perfect square integers between 1 and 81 inclusive?
1,4,9,16,25,36,49,64,81
What percentage of the integers 1 to 10 inclusive are not a multiple of 10?
90% of them.
