We roll a foursided die once and then we roll it as many tim

We roll a four-sided die once and then we roll it as many times as is necessary to obtain a different face than the one obtained in the first roll. Let the outcome of the experiment be (r1, r2) where r1 and r2 are the results of the first and the last rolls, respectively. Assume that all possible outcomes have equal probability. Find the probability that: (a) r1 is even. (b) Both r1 and r2 are even. (c) r1 + r2 < 5.

Solution

If Four sided die is rolled so possible outcomes are (1,2,3,4)

1). If r1 is even then outcome set is (2 ,4) = 2

      Here S=4 as die rolled 1^st time only

      Probability = 2/4 = ½

Again it rolled to get outcome other than 1 roll then

                  S= 4*3 = 12 (3= other than one digit from 1^st roll)

2. ) Both r1 & r2 are even then set is (2 , 4) = 2

        Probability = 2/12 = 1/6

3. ) r1+r2< 5 then set is (1,2,3,4) = 4

     Probability = 4/12=1/3