Answer to Question #259750 in Statistics and Probability for rtf

Question

A die that is loaded so that the numbers 1 and 3 are equally likely to appear and 2, 4, 5, and 6 are equally likely to appear. However, 1 is three times as likely to appear as 2.

(a) One die is rolled. Assign probabilities to the outcomes that accurately model the likelihood of the various numbers to appear.

(b) One die is rolled. What is the probability of getting a 3?

(c) One die is rolled. What is the probability of getting a 1 or a 4?

(d) One die is rolled. What is the probability of getting an even number?

Answer 1

First thing we should do is to estimate what probabilities is such a die has to roll each number. Let X be a random variable that represents the outcome. Let P(X = 2) is equal to x, then P(X = 2) = P(X = 4) = P(X = 5) = P(X = 6) = x, P(X = 1) = P(X = 3) = 3x

$4x + 6x = 1\implies x =0.1$

So, the probabilities of getting 2, 4, 5, 6 is equals to 0.1, while the probabilities of getting 1, 3 is equals to 0.3

(a) Lets demonstrate an obtained result using a table

(b) According to table P(X = 3) = 0.3

(c) P(X = 1) + P(X = 4) = 0.3 + 0.1 = 0.4

(d) P(X = 2) + P(X = 4) + P(X = 6) = 0.1 + 0.1 + 0.1 = 0.3