Instead of using the values {1,2,3,4,5,6}
on dice, suppose a pair of dice have the
following: {1,2,2,3,3,4} on one die and
{1,3,4,5,6,8} on the other. Find the
probability of rolling a sum of 2 with
these dice. Be sure to reduce.
[?]

Answer:

1/36

Step-by-step explanation:

it is the exact same as if both your dice had the numbers {1,2,3,4,5,6}

you said the SUM of the dice that is indicates the answer of the addition of two (or for that matter more) numbers,... the only numbers that would sum 2 is 1+1,... and because you only have two ones (one per die) the answer is the same as if they where die with normal numbers,...

The probability of rolling a sum of 2 with these dice is 1/36.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

Pair of dice have= {1,2,2,3,3,4}

Now,

The probability of rolling a sum of 2 with two dice is the same as the probability of rolling snake eyes, since the only way to get a sum of 2 is if both dice show a 11. The probability of rolling a 1 on a single die is 1/6, so the probability of rolling a 1 on both dice is (1/6) × (1/6) = 1/3612.

However, in this case, the dice are not standard six-sided dice, but have different numbers on their faces. The first die has {1,2,2,3,3,4} and the second die has {1,3,4,5,6,8}. The probability of rolling a 1 on the first die is still 1/6, but the probability of rolling a 1 on the second die is also 1/6. Therefore, the probability of rolling a sum of 2 with these dice is still (1/6) × (1/6) = 1/36.

This probability cannot be reduced any further, since 1 and 36 have no common factors other than 1.

Therefore, the probability will be 1/36.

Learn more about probability here;

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