Mathematics, 11.01.2020 00:31 kaylynn77

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)

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Answer from: jayyy1002

Probability that the sum of the dice will be even or a multiple of 3 is $\frac{5}{6}$

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:

$probability =\frac{\text { number of favorable outcomes }}{\text { total number of possible outcomes }}$

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,

$p(sum\ is\ even) = \frac{18}{36}$

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:

$p(\text{ sum is multiple of 3}) = \frac{12}{36}$

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)

$\rightarrow \frac{18}{36} + \frac{12}{36} = \frac{18+12}{36}\\\\\rightarrow \frac{30}{36} = \frac{5}{6}$

Thus probability that the sum of the dice will be even or a multiple of 3 is $\frac{5}{6}$

Answer from: Quest

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (

Answer from: Quest

It is blindness and randomization

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