Answer:
P(1) = 0.2857
P(2) = 0.1428
P(3) = 0.1428
P(4) = 0.1428
P(5) = 0.1428
P(6) = 0.1428
Step-by-step 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
