Final answer:
The probability of pulling out two triangles from a bag with various plastic shapes, with replacement, is calculated by multiplying the probabilities of drawing a triangle on each independent draw. Since the probability of drawing a triangle each time is 6/15, the combined probability is (6/15) × (6/15), which simplifies to 4/25.
Step-by-step explanation:
The question asks about the probability of pulling out two triangles from a bag with plastic shapes, which contains 6 triangles, 4 circles, and 5 squares. If the first shape is replaced before pulling out the second shape, each selection is an independent event. Hence, the probability for each draw remains unchanged.
Firstly, we calculate the probability of drawing a triangle on the first draw. Since there are 6 triangles in the bag and a total of 15 shapes (6 triangles + 4 circles + 5 squares), the probability of drawing a triangle on the first draw is 6/15.
Because the first shape is replaced, we have the same number of shapes for the second draw. Therefore, the probability of drawing a triangle on the second draw is also 6/15. To find the probability of both events happening one after the other, we multiply the two probabilities.
P(two triangles) = P(first triangle) × P(second triangle)
P(two triangles) = (6/15) × (6/15) = 36/225, which simplifies to 4/25 when reduced.
Thus, the probability of drawing two triangles with replacement is 4/25.