Question

Mail - Pekovic, Danilo - Outloo x C A Bookstore Employee is Choo x Desmos | Scientific Calculator → C webassign.net/web/Student/Assignment-Responses/last?dep=23539404 Are events Y and Z independent, mutually exclusive, or neither? Explain your answers. (a) We roll a standard (6-sided) die once. Y is "roll a 2" and Z is "roll a 4 or less". (b) We roll a standard (6-sided) die once. Y is "rolla 2" and Z is "roll an odd number". Show My Work (Optionan Submit Answer

Answer 1

SOLUTION (02 Y: "2011 a 2' 2: "poll a 4 or less." y = $ 23, 2= 31, 2, 3, 43, When we roll a standard (6-sided ) die once, He bossible outcomes are 1, 2, 3, 4, 5, 6. Sample space, S= { 1, 2, 3, 4, 5, 63. Each out come in the sample space is equally likely to occur. P (Y)= P(£23) = 1 PCZ) = pc {1, 2, 3, 43) = P(813) + P(423) + P($ 33) + PE£43) - 5 + → + 6 + 5 * Are y and z. independent ? YnZ = $23 n$ 1,2,3,4} = {23. Ans. Are plyn28 - P({23) = t & P(Y) P(Z) = 1 x 1 - Y and 2 are not independent. No 4 and 2 mutually exclusive? YAZ= $23041, 2, 3, 43 = 423 + 8 * y and Z are not mutually exclusive. Ars NO!

(6) Y: "rol1 a 2. Z: "poll an odd number" Y = $23, Z=8 1,3,53. * Are Y and Z mutually exclusive? Yn2= {230 & 1, 3,53 = 0 > Y and 2 are mutually exclusive. Ans: YES! X Are y and z independent ? p(YAZ) = p (0) = 0 Þ ply) PC 2) = P(423) Plf 1,3,53) Y and 2 ore not inclependent, Ang. NO!