What is the probability of picking a white marble if there is 4 white marbles and 4 black marbles

Anumber cube is rolled two times in a row. find the probability it will land on 2 on the first roll and a number greater then 4 on the second roll

Let event a = you roll an even number on the first cube.let event b = you roll a 6 on the second cube.are the events independent or dependent? why?

Consider the linear model for a two-stage nested design with b nested in a as given below. yijk=\small \mu + \small \taui + \small \betaj(i) + \small \varepsilon(ij)k , for i=1,; j= ; k=1, assumption: \small \varepsilon(ij)k ~ iid n (0, \small \sigma2) ; \small \taui ~ iid n(0, \small \sigmat2 ); \tiny \sum_{j=1}^{b} \small \betaj(i) =0; \small \varepsilon(ij)k and \small \taui are independent. using only the given information, derive the least square estimator of \small \betaj(i) using the appropriate constraints (sum to zero constraints) and derive e(msb(a) ).