When rolling two standard six-sided dice, what is the probability that the sum of the dice will be even or a multiple of 3? (show your work)

Probability that the sum of the dice will be even or a multiple of 3 is

Solution:

Given that two standard six sided dice are rolled

To find: probability that the sum of the dice will be even or a multiple of 3

The probability of an event is given as:

Let us first find probability that the sum of dice will be even

The total possible outcomes when two dice are rolled is:

{ (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)  }

total number of possible outcomes = 36

Here,

favorable outcome = sum of dice is even

favorable outcome = (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)

Therefore, number of favorable outcomes = 18

Therefore,

Let us first find probability that the sum of dice is multiple of 3

favorable outcome = sum of dice is multiple of 3

favorable outcome = (1, 2) , (1 , 5) , (2 , 1 ) , (2, 4) , (3 , 3) , (3 , 6) , (4 , 2) , (4 , 5) , (5 , 1) , (5 , 4) , (6 , 3) , (6 , 6)

Therefore, number of favorable outcomes = 12

Thus probability is given as:

Total probability that the sum of the dice will be even or a multiple of 3:

total probability = p( sum is even ) + p(sum is multiple of 3)

Thus probability that the sum of the dice will be even or a multiple of 3 is

the solution is the point

step-by-step explanation:

we have

> equation a

> equation b

adds equation a and equation b

substitute the value of x in equation b to find the value of y

the solution is the point

no because mercury has a density of 13.6 grams per centimeter squared while gold has 19.32 grams centimeter squared

step-by-step explanation: