Question

In Exercises 1-2 are detailed some of the nefarious dicing practices of the Win Some/Lose Some Casino. In each case, find the probabilities of all the possible outcomes and also the probability that an odd number or an odd sum faces up.
1. Some of the dice are specially designed so that 1 and 6 never come up and all the other outcomes are equally likely.
2. Other dice are specially designed so that 1 comes up half the time, 6 never comes up, and all the other outcomes are equally likely.

Answer 1

The events which never occur will have probability zero. The probability of 2,3,4,5 occur will have 1/4 as they have equally likely chances of occurrence.

To find: The of all the probabilites possible outcomes and also odd sum faces an up. •come and I and 6 never All the occur is zero. the proo bability that an odd number on 1. Given: Poobcibility that up all other outcomes are equally likely possibilities or possible outcomes of a dice is s={1,2,3,4,5,63 The probabilities are given by ACID=o and PC6)=0 [given that I and 6 never occue? That is, poobability that I and o of 2, 3,45 PC@= since Occulance 1 - P(3) = P(4)=P(5), is equally likely Probability that odd number or an add sum faces up can be calculated as follows: outcomes of odd number or and odd sum {3,5:13 Probability that odd number or an add sum faces up but because probability occurrance of 1 is zelo. 4 faces up is Is 2