An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered $1, 2, 3, \ldots, 9$ is randomly picked and the number on the card is noted. The probability that the noted number is either $7$ or $8$ is: