explain how the answer to this is 2/9?

Question

determine the probability of rolling either a 7 or 11 on a single toss for a pair of dice.

Answer 1

There are 36 possible outcomes when rolling 2 dice (6*6). There are 8 possible ways to roll 7 or 11 (1.6, 2.5, 3.4, 4.3, 5.2, 6.1, 6.5, 5.6). So, to get the probability, you divide the 8 ways to get 7 or 11 by the 36 possible rolls which gives you 8/36=2/9

Answer 2

That would mean that for each time you roll the dice, you have an 8 in 36 chance of rolling one of those two numbers. 7 gives a 6 in 36 chance (1 in 6), and 11 gives a 2 in 36 chance (1 in 18), so that is completely correct. Added together, the twain equal 8/36, which simplifies to 2/9 (divide by 4/4)

Answer 3

The probability is P(7) + P(11).

P(7) = 6/36 {1, 6; 2, 5; 3, 4; 4, 3; 5, 2; 6, 1}
P(11) = 2/36 {5, 6; 6, 5}

Add them together to get 8/36 = 2/9.

Answer 4

DICE ODDS
2 =1 IN 36
3 =2 IN 36 (SAME AS 1 IN 18 ROLLS)
4 =3 IN 36
5 =4 IN 36 (SAME AS 1 IN 9 ROLLS)
6 =5 IN 36
7 =6 IN 36 (SAME AS 1 IN 6 ROLLS)
8 =5 IN 36
9 =4 IN 36 (SAME AS 1 IN 9 ROLLS)
10=3 IN 36
11=2 IN 36 (SAME AS 1 IN 18 ROLLS)
12=1 IN 36

Answer 5

If you use a spreadsheet or calculator you can solve this. a) Add up all the throws & divide into 9, the number of 2's. Multiply the fraction by 100, or shift the decimal 2 places for %. b) Total the odd numbered throws, divide by total throws, as before. c) Add throws 4, 5, & 6, divide as before, for %. d) Normal expectation for any number is 100/6. e) Half the numbers are odd, so 500 times.

Answer 6

Imagine a black die and a white die. How many different results can happen? 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 2-1, 2-2, 2-3, etc.

Now, how many of these add up to 7 or 11?

Answer 7

that is incorrect i believe