The probability of choosing a brown pair of gloves is 1/3, as there are 3 options and only 1 of them is brown. The probability of choosing a red hat is 1/2, as there are 2 options and only 1 of them is red. The probability of choosing any scarf is 1, since she will definitely choose one. So, the probability of Tamara choosing a pair of brown gloves and a red hat is:
1/3 (for brown gloves) x 1/2 (for red hat) x 1 (for any scarf) = 1/6
Therefore, the answer is option D, one-sixth.