Question

A red die and a blue die are thrown. Both dice are loaded (that is, not all sides are equally likely). Rolling a 1 with the red die is twice as likely as rolling each of the other five numbers and rolling a 3 with the blue die is twice as likely as rolling each of the other five numbers. a. (2.5 pt.) What is the probability of each outcome of the red die

Answer 1

P(1) = 0.2857

P(2) = 0.1428

P(3) = 0.1428

P(4) = 0.1428

P(5) = 0.1428

P(6) = 0.1428

Explanation:

From the question, we know that Rolling a 1 with the red die is twice as likely as rolling each of the other five numbers, so we can write the following equation:

P(1) = 2X

Where X is the probability of rolling each of the other five numbers or:

P(2) = P(3) = P(4) = P(5) = P(6) = X

Additionally, the sum of all the probabilities is 1, so:

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

Now, we can replace P(1) by 2X and P(2), P(3), P(4), P(5) and P(6) by X, as:

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

2X + X + X + X + X + X = 1

Finally, solving for X, we get:

7X = 1

X = 1/7

X = 0.1428

So, the probability of rolling a 1 is equal to:

P(1) = 2X = 2*(0.1428) = 0.2857

And the probability of rolling each of the other five numbers is:

P(2) = P(3) = P(4) = P(5) = P(6) = X

P(2) = P(3) = P(4) = P(5) = P(6) = 0.1428