Q:

PLS HELP ME ASAP A six-sided fair die is rolled two times. Arrange the events in order from the event with the highest probability to the event with the lowest probability.1.the probability of getting thesame number on each roll.2.the probability of obtaining anodd prime number (excluding1) on each roll.3.the probability that thedifference of the two numbersis at most 1.4.the probability that thesecond number is a multipleof the first number

Accepted Solution

A:
Answer:event 2 > event 4> event 1> event 2Step-by-step explanation:Probability of getting an event = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]Total outcomes of rolling a dice twice = 36{1,1};{1,2};{1,3};{1,4};{1,5};{1,6}{2,1};{2,2};{2,3};{2,4};{2,5};{2,6}{3,1};{3,2};{3,3};{3,4};{3,5};{3,6}{4,1};{4,2};{4,3};{4,4};{4,5};{4,6}{5,1};{5,2};{5,3};{5,4};{5,5};{5,6}{6,1};{6,2};{6,3};{6,4};{6,5};{6,6}1)The probability of getting the  same number on each roll.Favorable events : {1,1};{2,2};{3,3};{4,4};{5,5};{6,6} = 6So, probability of getting the  same number on each roll= [tex]\frac{6}{36}[/tex]2)the probability of obtaining an  odd prime number (excluding  1) on each roll.Favorable events : {3,3};{3,5};{5,3};{5,5} = 4So, the probability of obtaining an  odd prime number (excluding  1) on each roll = [tex]\frac{4}{36}[/tex]3)the probability that the  difference of the two numbers  is at most 1.So, we are supposed to find the probability of getting the number whose  the difference  is less than or equal to 1 Favorable events : {1,1};{1,2};{2,1};{2,2};{2,3};{3,2};{3,3};{3,4};{4,3};{4,4};{4,5};{5,4};{5,5};{5,6};{6,5};{6,6} =16So, the probability that the  difference of the two numbers  is at most 1 = [tex]\frac{16}{36}[/tex]4)the probability that the  second number is a multiple  of the first numberFavorable events : {1,1};{1,2};{1,3};{1,4};{1,5};{1,6};{2,2};{2,4};{2,6};{3,3};{3,6};{4,4};{5,5};{6,6}=14So, the probability that the  second number is a multiple  of the first number = [tex]\frac{14}{36}[/tex]Probabilities in decreasing order : [tex]\frac{16}{36}>\frac{14}{36}>\frac{6}{36}>\frac{4}{36}[/tex]The event with the highest probability to the event with the lowest probability : event 2 > event 4> event 1> event 2Hence , the events in order from the event with the highest probability to the event with the lowest probability is event 2 > event 4> event 1> event 2