4. (a) Write down the conditions under which the binomial distribution may be a suitable model to use in statistical work. A six-sided die is biased. When the die is thrown the number 5 is twice as likely to appear as any other number. All the other faces are equally likely to appear. The die is thrown repeatedly. Find the probability that
(b) (i) the first 5 will occur on the sixth throw,
(ii) in the first eight throws there will be exactly three 5 s .