Respuesta :
Given that
If two fair dice are rolled then we have to find the probability of the total showing either even or less than 5.
Explanation -
If a dice is rolled then the total outcomes are 6.
As it is given that 2 dice are rolled then the total outcome will be
Total outcome = 6 x 6 = 36
There are 2 cases -
Case 1 - Total is even
This is possible only when both the dices show both the numbers even or odd.
So, these cases will be (1,1),(1,3), (1,5), (2,2), (2,4),(2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1),(5,3), (5,5), (6,2), (6,4), (6,6)
These are a total of 18 outcomes.
Case 2- Total is less than 5
These will be (1,1), (1,2), (1,3), (2,1), (2,2), (3,1)
From these, we have counted (1,1), (1,3), (2,2), and (3,1) in case 1. So we will have only
2 additional outcomes.
Hence the favourable outcome for total being even or less than 5 is = 18 + 2 = 20
Therefore the probability will be
[tex]P=\frac{favourable\text{ outcome}}{Total\text{ outcomes}}[/tex][tex]P=\frac{20}{36}=\frac{5}{9}[/tex]So option B is correct.
Final answer -
Therefore the final answer will be 5/9.