Question

2 dice one red other blue are thrown simultaneously. find the probability of (1) getting sum of numbers on the upper faces greater than 5. (2) getting the score of the second die greater than the score on the first die​

Answer 1

Answer:

(1) 13/ 18

(2) 5/12

Step-by-step explanation:

(1)

If any die rolls a 5 or 6 it automatically guarantees a sum greater than 5, as for any no the other die rolls, the sum is always greater than 5

∴ 12 possibilities (6 for rolling 5 and 6 for rolling 6)

If a die rolls a 4, then the other die should roll a no greater than or equal to 2

∴ 5 possibilities

If a die rolls a 3, then the other one should roll 3 or greater

∴ 4 possibilities

if a die rolls a 2, then the other one should roll 4 or greater

∴ 3 possibilities

If a die rolls a 1, the other one should roll 5 or greater

∴ 2 possibilities

so total no of possibilities for sum to be greater than 5 is 26

and no of possible combinations is 36

∴ probability is 26/36 = 13/18

(2)

If the first die rolls a 1, then the second die rolls a greater no if it rolls 2 or above

∴ 5 possibilities

If the first die rolls a 2, then the second die rolls a greater no if it rolls 3 or above

∴ 4 possibilities

If the first die rolls a 3, then the second die rolls a greater no if it rolls 4 or above

∴ 3 possibilities

If the first die rolls a 4, then the second die rolls a greater no if it rolls 5 or above

∴ 2 possibilities

If the first die rolls a 5, then the second die rolls a greater no if it rolls 6

∴ 1 possibilities

If the first die rolls a 6, then the second die can't roll greater

∴ 0 possibilities

Total possibilities for our condition to be true  = 0+1+2+3+4+5= 15

total combination = 36

∴ probability of our condition being true = 15/36= 5/12

As far I can tell, we have to do one by one as it involves summation, so combination and permutation can't reduce the answer by much.....

Hope this helps...