Question

Mina has 6 different skirts, 3 different scarfs and 7 different tops to wear. She has exactly one orange scarf, exactly one blue skirt, and exactly one black top. If Mina randomly selects each item of clothing, find the probability that she will wear those clothings for the outfit.

(a) \(\frac{1}{321}\)

(b) \(\frac{1}{126}\)

(c) \(\frac{4}{411}\)

(d) \(\frac{2}{73}\)

The question was asked by my school teacher while I was bunking the class.

The question is from Multiplication Theorem on Probability topic in section Discrete Probability of Discrete Mathematics

Answer 1

Right option is (b) \(\frac{1}{126}\)

Easy explanation: There is a \(\frac{1}{3}\) probability that Mina would randomly select the orange scarf, a \(\frac{1}{6}\) probability to select the blue skirt, and a \(\frac{1}{7}\) probability to select the black top. These events are independent, that is, the selection of the scarf does not affect the selection of the tops and so on. Hence, the probability that she selects the clothings of her choice is \(\frac{1}{3} * \frac{1}{6} * \frac{1}{7}\) = 126.