5. (a) Consider an unfair dice with 5 sides numbered 1, 2, 3, 4 and 5. With this dice, any two numbers greater than 2 ha

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5 A Consider An Unfair Dice With 5 Sides Numbered 1 2 3 4 And 5 With This Dice Any Two Numbers Greater Than 2 Ha 1 (42.79 KiB) Viewed 23 times

5. (a) Consider an unfair dice with 5 sides numbered 1, 2, 3, 4 and 5. With this dice, any two numbers greater than 2 have the same probability of getting rolled, and the numbers 1 and 2 are both twice as likely of getting rolled as the number 3. In an experiment this loaded dice is rolled once and the value thus ob- tained is recorded. Let (12,p) denote the probability model of this exper- iment. Let A be the event "an even number is rolled" and B be the event "a number less than 4 is rolled". (1) Determine the probability of rolling an x for each possible value of (ii) Compute p(A). (iii) Compute p(4B). (If you did not answer question (i), you can attempt questions (ii) and (ii) by taking p(1) = p.p(5) = pa, and use Pups instead of actual values.) (b) We consider a group of 120 sheep and cows, and assume that they can only be white or black. The numbers of animals of these two colours are as follows: White Black Total Sheep 60 12 72 Cows 10 18 28 Total 70 One animal is selected at random (we assume that each animal is equally likely to be selected). Compute the probability: (i) That it is white. (ii) That is it white, given that it is a cow. 30 120