Answer: The probability P(A or B) that the garment she chooses is pink or a shirt is 0.56 (or 56%)
Step-by-step explanation: The total number of possibilities is defined by the contents of Iman's wardrobe. What she has includes, one blue shirt, one pink shirt, one blue hat, one blue belt, one blue pair of pants, and one pink pair of pants. Altogether, she has six possibilities available to her. Of all these she has two pink garments and four blue garments, and two shirts.
The probability that she chooses a pink garment P(A) is derived as,
P(A) = Number of required outcomes/Number of all possible outcomes
P(A) = 2/6
P(A) = 1/3
The probability that she chooses a shirt P(B) is derived as,
P(B) = Number of required outcomes/Number of all possible outcomes
P(B) = 2/6
P(B) = 1/3
Also the probability of P(A) and P(B) is derived as
P(A and B) = P(A) x P(B)
P(A and B) = 1/3 x 1/3
P(A and B) = 1/9
Therefore, the probability P(A or B) that what she chooses is pink or a shirt is derived as follows;
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = (1/3 + 1/3) - 1/9
P(A or B) = 2/3 - 1/9
P(A or B) = 6/9 - 1/9
P(A or B) = 5/9
P(A or B) = 0.5556
P(A or B) ≈ 0.56 (or 56%)
Therefore the probability that the garment she chooses is pink or a shirt is 0.56 or (56 percent)
