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15/49

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There are 15 prime numbers between 1 and 49 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47). If you randomly choose one natural number from the 49 numbers between 1 and 49 inclusive, there is a 15/49 probability that it will be prime.

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Q: What is the probability of prime numbers being chosen randomly from the number 1-49?
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What is the probability that the number 23 will be randomly picked out of 100?

Assuming then that there are 100 numbers, 1-100, the probability of the number 23 being randomly picked out of 100 is: 1/100 or 0.01.


What is the probability of getting tails and selecting a 3 if you toss a coin and randomly select a number?

There are infinitely many numbers and so the probability of the second event is 0. As a result the overall probability is 0.


If a number from 1 to 20 is chosen what is the probability of getting 7?

1 out of 20 this is because there are 20 numbers in total, and there is only one 7 in there. (Assuming that there is the same probability for each number to be chosen, and that 17 is excluded as an affirmative outcome)


If a number is chosen at random from the numbers 1 to 20 inclusive what is the probability a prime will be picked?

There are 8 out of 20 numbers that are prime, so 8/20, or 2/5.


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".

Related questions

A number is chosen at random from the first 20 positive whole numbers What is the probability that it is not a prime number?

There are 12 composite (and 8 primes) in the first twenty whole numbers. So the probability of randomly choosing a non-prime is 12/20 or 60%.


A number is randomly chosen between 1-50 what is the probability of selecting multiples of 36?

It is 0.02


What is the probability that the number 23 will be randomly picked out of 100?

Assuming then that there are 100 numbers, 1-100, the probability of the number 23 being randomly picked out of 100 is: 1/100 or 0.01.


A nursing class has 13 women and 18 men If a student is chosen randomly to be the team leader what is the probability the student is a woman?

The probability that a randomly chosen student is a woman can be calculated by dividing the number of women by the total number of students in the class. In this case, there are 13 women and 31 total students, so the probability is 13/31, which simplifies to approximately 0.419 or 41.9%.


What is the probability of getting tails and selecting a 3 if you toss a coin and randomly select a number?

There are infinitely many numbers and so the probability of the second event is 0. As a result the overall probability is 0.


One number is chosen at random from the whole numbers 1 to 100 inclusiveWhat is the probability that the number is not prime?

3 out of 4


One number is chosen at random from the whole numbers 1 to 100 inclusiveWhat is the probability that the number has two digits?

90%


If a number from 1 to 20 is chosen what is the probability of getting 7?

1 out of 20 this is because there are 20 numbers in total, and there is only one 7 in there. (Assuming that there is the same probability for each number to be chosen, and that 17 is excluded as an affirmative outcome)


What is the probability of a prime number being picked randomly from the numbers 1 - 15?

Prime numbers from 1 to 15 are: 2 3 5 7 11 and 13 So the probability is: 6/15 or as 2/5


What is the probability of a prime number being picked randomly from the numbers 1 through 49?

There are 15 primes from 1 to 49 (including '1').The probability is (15/49) = 30.612 %(rounded)


What is the Probability that if a number is chosen the number is even?

50%


A number is chosen at random from the first twelve whole numbers. What is theThe probability that it is isExactly divisible by 3?

1/3