Number of positive integers not exceeding 100 and divisible by 3 are = 33
The favorable points are { 3, 6, 9, 12, ....99}
Total number of positive integers not exceeding 100 = 100
The probability that a positive integer not exceeding 100 selected at random is divisible by 3 is
What is the probability that a positive integer not exceeding 100 selected at random is divisible...
8. (i) How many positive integers not exceeding 200 that are divisible by 3 or 5 are there? (ii) What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who come from the same state?
8) A number is selected at random from (1,2,.. , 100). Given that the number selected is divisible by 2, find the probability that it is divisible by 3 or 5.
A 3-digit positive integer N is randomly chosen. Compute the probability of the event that (a) N is divisible by 3. (b) N is divisible by 3 if its leftmost digit is 1.
1. Let n be a positive integer with n > 1000. Prove that n is divisible by 8 if and only if the integer formed by the last three digits of n is divisible by 8.
33. Prove that 11n - 6 is divisible by 5 for every positive integer n.
a random sample of 100 us individuals were selected from a population. the probability of having hypertension is about 24%. What is the probability that there are at most 30 people in the sample who have hypertension? Round to 3 decimal places
Problem of the Week #4 1. An integer bis said to be divisible by an integer a 0, in symbols ab. if there exists some integer c such that b = ac. In other words, b is divisible by a if a goes into b with no remainder. For example, 30 is divisible by 5 (in symbols, 5 30 ) because 30 = 5 x 6. Problem of the Week: The following integers are all divisible by 31: 28272, 27683,...
Prove that if an integer n is not divisible by 3, then n^2=3k+1 for some integer k. Note: “not divisible by 3” means either “n=3m+1 for some integer m” or “n=3m+2 for some integer m”.
If a button has a life exceeding 100,000 button presses with probability 0.79, what is the probability that a set of 100 buttons on a controller will all last longer than 100,000 presses?
1) Let n and m be positive integers. Prove: If nm is not divisible by an integer k, then neither n norm is divisible by k. Prove by proving the contrapositive of the statement. Contrapositive of the statement:_ Proof: Direct proof of the contrapositive