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
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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