Anumber is chosen at random from the first 100 positive integers. find the probability that the number chosen is prime.

1/5

1/4

1/3

The answer is B). 1/4

Step-by-step explanation:

The probability that the number chosen is prime is:

The probability of an event is defined as the ratio of number of favorable outcome to the total number of outcomes.

Here the total number of outcomes are: 100

( Since we have to take first 100 positive integers i.e. 1-100)

Also, the number of favorable outcomes i.e.  the number of prime numbers between 1-100 is: 25

( Since, the prime numbers are:

2,3,5,7,11,13,17,19,23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 )

Hence, the probability that the number chosen is prime is:

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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