Sebastian has a bag of 15 blue marbles, 18 red marbles, and 12 yellow marbles. He reaches into the bag three times and pulls out 2 red marbles and a blue marble. What is the probability that he reaches into the bag and pulls out a yellow marble next? A. 1/4 B. 8/21 C. 2/7 D. 5/14

Explanation:

Initially there are 15+18+12 = 45 marbles total. He selects 3 marbles (2 reds, 1 blue).

Assuming he doesn't put the three marbles back, this means there are now 45-3 = 42 marbles overall. The yellow count hasn't changed since the first three marbles do not involve yellow. We have 12 yellow out of 42 which leads to the fraction 12/42 to represent the probability of getting yellow.

Reduce 12/42 to get 2/7. You divide both parts by the GCF 6.

Side note: if he did put the marbles back, then the probability of getting yellow would be 12/45 = 4/15

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq