Sage-Tips

What is the probability that a randomly selected integer chosen from the first 1 00 positive integers is odd?

What is the probability that a randomly selected integer chosen from the first 100 positive integers is odd? Ans: 50/100.

What is the probability that a positive integer not exceeding 100 selected at random is divisible by 5 or 7?

What is the probability that a positive integer not exceeding 100 selected at random is divisible by 5 or 7? There are: ⌊100/5⌋ = 20 positive integers divisible by 5. ⌊100/7⌋ = 14 positive integers divisible by 7.

What is the probability that a randomly selected positive integer is prime?

The primes that are less than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47. There are 15 primes less than or equal to 50. Thus the probability that a prime is selected at random is 15/50 = 30\%.

What is the probability that a number selected at random from a set of the first 50 positive integers is divisible by 4?

So 4/50 = 2/25 = 8\% is the probability of a uniformly chosen random number in that range being a multiple of both 3 and 4.

What is the probability that the sum of the numbers on two dice is even when they are rolled?

Thus, we have P(even sum)=1/2(P(first was even)+P(first was odd))=1/2(1)=1/2.

What is the probability that a positive integer not exceeding 100 selected at random is divisible by?

100 7 = 14.2857 … \dfrac{100}{7}=14.2857\dots 7100​=14.2857… , then there are 14 occurrences of a positive integer not exceeding 100 that is divisible by 7.

How many positive integers not exceeding 100 and are divisible by neither 5 nor 7?

68 numbers
So, there are exactly 68 numbers not exceeding 100 that are not divisible by 5 or by 7.

What is the probability of picking a prime number between 41 and 50 inclusive?

There are 15 primes less than or equal to 50. Thus the probability that a prime is selected at random is 15/50 = 30\%.

Is selected at random from first 50 natural numbers then the probability that it is a multiple of 3 and 4 is?

Hence, the Probability of getting a number which is a multiple of 3 and 4 is 2/25.

What is the probability of a random variable being less than?

The probability of a random variable being less than or equal to a given value is calculated using another probability function called the cumulative distribution function. A cumulative distribution function (CDF), usually denoted F ( x), is a function that gives the probability that the random variable, X, is less than or equal to the value x.

Can the probability of an event be negative?

Since probabilities are never negative, the probability of one event or another is always at least as large as either of the individual probabilities.

What is the difference between discrete and non discrete random variables?

A random variable that takes on a finite or countably infinite number of values (see page 4) is called a dis- crete random variable while one which takes on a noncountably infinite number of values is called a nondiscrete random variable.

What is the probability mass function of a discrete random variable?

If the random variable is a discrete random variable, the probability function is usually called the probability mass function (PMF). If X is discrete, then f ( x) = P ( X = x).