Every morning, Rosencrantz flips a coin. If it turns up heads, he rises out of bed and rolls two dice to decide what he will have for breakfast. If the sum of the dice is more than 8 he has eggs, otherwise he has cereal. If the coin turns up tails, Rosencrantz sleeps for another hour and then has eggs for breakfast. (a) Assuming a fair coin and fair dice, what is the conditional probability that Rosencrantz eats cereal for breakfast given that the coin flip turned up heads