An unbiased coin is tossed. If the result is head, a pair of unbiased dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well-shuffled pack of eleven cards numbered 2, 3, …, 12 is picked and the number on the card is noted. What is the probability that the noted number is either 7 or 8?
