DiscussionWeek5_Data605

Chapter 1.2

6. 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 example, a six is three times as probable as a two.) What is the probability of getting an even number in one throw?

d=dot

even dots are 2d, 4d, 6d

So, we are looking for the probability \(P(2d) + P(4d) + P(6d)\)

\(6m(1d) = 5m(2d) = 4m(3d) = 3m(4d) = 2m(5d) = 1m(6d)\)

\(6m(1d) + 5m(2d) + 4m(3d) + 3m(4d) + 2m(5d) + m(6d) = 1\)

\(1/6m(6d) + 2/6m(6d) + 3/6m(6d) + 4/6m(6d) + 5/6m(6d) + 6/6m(6d) = 1\)

\(21/6m(6d) = 1\)

\(m(6d) = 6/21\)

\(m(4d) = (6/21) / (6/4) = 4/21\)

\(m(2d) = (6/21) / (6/2) = 2/21\)

\(P(2d) + P(4d) + P(6d) = 6/21 + 4/21 + 2/21 = 12/21\)

The probability of an even roll of a dice is 12/21 or 0.57%.