Question

Neha has 4 yellow t-shirts, 6 black t-shirts, and 2 blue t-shirts to choose from for her outfit today. She chooses a t-shirt randomly with each t-shirt equally likely to be chosen. Find the probability that a black or blue t-shirt is chosen for the outfit.

(a) \(\frac{8}{13}\)

(b) \(\frac{5}{6}\)

(c) \(\frac{1}{2}\)

(d) \(\frac{7}{12}\)

I have been asked this question in unit test.

My question is taken from Addition Theorem on Probability in division Discrete Probability of Discrete Mathematics

Answer 1

Correct option is (c) \(\frac{1}{2}\)

To explain: Define the events A and B as follows: A=Neha chooses a black t-shirt. B= Neha chooses a blue skirt. Neha cannot choose both a black t-shirt and a blue t-shirt, so the addition theorem of probability applies:

P(A U B) = P(A) + P(B) = \((\frac{6}{12}) + (\frac{2}{12}) = \frac{3}{6} = \frac{1}{2}\).