Question

1. (partially visible) tossed a coin three times. which tree diagram shows all of the possible outcomes of the coin landing heads up or tails up? (tree diagrams labeled a, g, h, j are shown) 2. a teacher has a container of paper clips. she will randomly select one paper clip from the container. the container has: - 8 pink clips - 14 purple clips - 12 yellow clips - 16 blue clips which statement is true? a the probability of selecting a purple paper clip is \\(\frac{3}{4}\\), and the probability of selecting a paper clip that is not purple is \\(\frac{1}{4}\\). b the probability of selecting a purple paper clip is \\(\frac{1}{4}\\), and the probability of selecting a paper clip that is not purple is \\(\frac{3}{4}\\). c the probability of selecting a purple paper clip is \\(\frac{18}{25}\\), and the probability of selecting a paper clip that is not purple is \\(\frac{7}{25}\\). d (partially visible) the probability of selecting a purple paper clip is \\(\frac{7}{25}\\), and the probability of selecting a paper clip that is not purple is \\(\frac{18}{25}\\).

Explanation:

Step1: Calculate total paper clips

Add all paper clip counts: $8 + 14 + 12 + 16 = 50$

Step2: Find purple probability

Divide purple clips by total: $\frac{14}{50} = \frac{7}{25}$

Step3: Find non-purple probability

Subtract purple probability from 1: $1 - \frac{7}{25} = \frac{18}{25}$

Step4: Match to correct option

Compare results to given choices.

Answer:

D. The probability of selecting a purple paper clip is $\frac{7}{25}$, and the probability of selecting a paper clip that is not purple is $\frac{18}{25}$