Please just solve the 4th question. The correct answer should be 27. My question is : I tried to calculate the expected number of throwing and got (1+p)p^2 ( p= the probability of getting 6) and I was correct. But, could you show me how to get to the correct answer? Thank you

You have a fair coin and 2 dice. The first die is fair and the second die is biased as follows:the probability of getting 6 equals = and the rest outcomes are equally probable. We toss the coin first. If the result is tail, we choose the first die for our experiment. Otherwise, we use the second die. And then we roll the die once. (i) (2 points) For the second die, find the probability of getting 1, 2, .. . 6. (ii) (3 points) What is the probability that the rolled die showed a 6. (iii) (5 points) If the rolled die showed a 3, what is the probability that the coin showed " Tail"? (iv (5 points) We throw the chosen die until we get two consecutive 6. What is the expected number of throws needed? Solution (You can use the back of the page too)