Question

A die is loaded in such a way that the probability of each face turning up is proportional to the number of dots on that face. For instance, a six is three times as probable as a two. What is the probability of rolling a three?

1) 1/21
2) 1/15
3) 1/10
4) 1/6

Answer 1

A loaded die is one where the probability of each face turning up is not equal. In this case, the probability of each face is proportional to the number of dots on that face. To find the probability of rolling a three in this loaded die, we need to determine the proportion of the probability that a three has compared to the probabilities of all the other faces. However, without knowing the probabilities of the other faces, we cannot determine the exact value of the probability of rolling a three.

Step-by-step explanation:

A loaded die is one where the probability of each face turning up is not equal. In this case, the probability of each face is proportional to the number of dots on that face. For example, if a six is three times as probable as a two, then the probability of rolling a two is 1/3 of the probability of rolling a six.

To find the probability of rolling a three in this loaded die, we need to determine the proportion of the probability that a three has compared to the probabilities of all the other faces. Let's call the probability of rolling a three as P(3). We can set up the following proportion:

P(3) / P(6) = 3 / 1

Since the probabilities of all faces must add up to 1, we can write the equation as:

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

Substituting the proportion we found earlier, we have:

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

By rearranging the equation, we have:

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

To solve for P(3), we need the probabilities of the other faces. Since we don't have that information, we cannot determine the exact value of P(3).