Pls 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 the same number on each roll. 2.the probability of obtaining an odd prime number (excluding 1) on each roll. 3.the probability that the difference of the two numbers is at most 1. 4.the probability that the second number is a multiple of the first number

event 2 > event 4> event 1> event 2

Step-by-step explanation:

Probability of getting an event =

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} = 6

So, probability of getting the  same number on each roll=

2)the probability of obtaining an  odd prime number (excluding  1) on each roll.

Favorable events : {3,3};{3,5};{5,3};{5,5} = 4

So, the probability of obtaining an  odd prime number (excluding  1) on each roll =

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} =16

So, the probability that the  difference of the two numbers  is at most 1 =

4)the probability that the  second number is a multiple  of the first number

Favorable 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}=14

So, the probability that the  second number is a multiple  of the first number =

Probabilities in decreasing order :

The event with the highest probability to the event with the lowest probability : event 2 > event 4> event 1> event 2

Hence , 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

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq