1. A six-sided die is biased in that the probability of a face is proportional t

Question

1. A six-sided die is biased in that the probability of a face is proportional to the number of dots in that face. Consider the random experiment of rolling this die once. (a) What is the sample space of this experiment? (b) Considering the assumption regarding this die, determine the probabilities of each of the outcomes in this experiment. Hint: Recall that the total probability of all the outcomes must sum to 1.] (c) What is the probability of the compound event A, which is that the outcome is a face with an even number of dots? (d) What is the probability of event B, which is the event that we get at least 4 dots? (e) What is the probability that either A or B or both occur, that is, of PrIAUB?

Explanation / Answer

a) Sample space => {1,2,3,4,5,6}

b) Each of the 6 has got equal probability of occurance

Thus, P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = 1/6

c) A=> {2,4,6}

Thus, 3 cases out of 6 are even

Thus, P(A) = 3/6 =1/2

d) atleast 4 dots means, 4,5,6. Thus, B= {4,5,6}

P(B) = 3/6 = 1/2

e) A=> {2,4,6} and B=>{4,5,6)

Thus, A U B => {2,4,5,6}

Thus required probability = 4/6 = 2/3

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