Two dices were thrown in a single toss. What is the probability that they will show:
1. Sum of 8
2. Sum of 5
3. Sum of 7 or 8
4. Not obtaining 9
5. At least 10.

1)5/36

2)1/9

3)11/36

4)8/9

5)1/6

Step-by-step explanation:

E: throwing two dice

Two dice thrown in a single toss,

in this event the outcomes may

be (1,1),(1,2)(1,6),(2,1)(2,6),(3,1)(6,6)

total 6×6 outcomes: 36 outcomes

here,total possible outcome is 36

P(of anything)=(Total no. of favourable outcome/total possible outcome)

now, (1)sum of 8

we get sum of 8 only when it comes

(2,6),(3,5),(4,4),(5,3),(6,2)

Total no. of favourable outcome is 5

P(getting sum of 8)= 5/36

2) sum of 5

we get sum of 5 only when it comes

(1,4),(2,3),(3,2),(4,1)

Total no. of favourable outcome is 4

P(getting sum of 5)= 4/36=1/9

3)sum of 7 or 8

we get sum of 8 only when it comes

(2,6),(3,5),(4,4),(5,3),(6,2)

or, get 7 when it comes

(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

Total no. of favourable outcome is 11

P(getting sum of 7 or 8)= 11/36

4)sum to be not 9

we get sum of 9 only when it comes

(3,6),(4,5),(5,4),(6,3)

Total no. of favourable outcome is 4

P(getting sum of 9)= 4/36=1/9

here,we have to find probability of getting (not 9),

which is equal to : 1- probability of getting 9

=1 -1/9= 8/9

5) At least 10

atleeast 10 includes 10 to maximum (12)

i.e, 10,11&12

fav outcome: (4,6),(5,5)(6,4) & (5,6),(6,5) & (6,6)

total no. of fav outcome is 6

probability (atleast 10)=6/36 =1/6

✌️:)

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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