Need an answer to the question circled, thanks. (a) A four-faced dice numbered 3

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Need an answer to the question circled, thanks.

(a) A four-faced dice numbered 3, 4, 5, and 6 is rolled two times. (i) Draw a tree diagram to show all the possible outcomes with the respective probabilities shown on the branches. (ii) What is the probability that both numbers appeared on the top are even? (iii) What is the probability that the numbers are different? (iv) Find the probability that the second number is a 4, given that the first is odd. Sebiji dadu yang mempunyai 4 permukaan dan dinomberkan 3, 4, 5 dan 6 dilambungkan dua kali. (i) Lukiskan sebuah rajah pokok untuk menunjukkan semua kesudahan yang mungkin dengan kebarangkalian yang sepadan ditunjukkan pada cabangnya. (ii) Apakah kebarangkalian kedua-dua nombor pada permukaan at as adalah genap? (iii) Apakah kebarangkalian nombor-nombor itu adalah berlainan? (iv) Carikan kebarangkalian number kedua adalah 4, diberi bahawa nombor pertama ialah ganjil. (b) The length, x cm, of aluminum bars produced by a factory follows a normal distribution. A random sample of 8 bars is selected and their lengths have the following information: sigma x = 274; sigma x^2 = 9391. (i) Find the mean and standard deviation of this sample.

Explanation / Answer

3.4.5.6 rolled two times

b) probability that both numbers are even

probability that number is even on one dice = 2/4 = 1/2

hence required probability= 1/2*1/2 = 1/4

c) probability that numbers are different = 4/4*3/4 = 3/4

{first dice any number ,on 2nd dice ,each number except the number which cameon 1st dice =3/4}

d)probability that 2nd number is 4 given 1st number is odd = 1/4

as the event A and event B is independent

A - getting number on 1st dice

B -getting number on 2nd dice

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