a spinner has two equal sections, one green and one orange. the spinner is spun three times, resulting in…

a spinner has two equal sections, one green and one orange. the spinner is spun three times, resulting in the sample space s = {ggg, ggo, gog, ogg, goo, ogo, oog, ooo}. if the random variable x represents the number of times orange, o, is spun, which graph represents the probability distribution? probability distribution probability distribution

a spinner has two equal sections, one green and one orange. the spinner is spun three times, resulting in the sample space s = {ggg, ggo, gog, ogg, goo, ogo, oog, ooo}. if the random variable x represents the number of times orange, o, is spun, which graph represents the probability distribution? probability distribution probability distribution

Answer

Explanation:

Step1: Calculate total number of outcomes

The sample - space has 8 elements, so (n(S)=8).

Step2: Calculate (P(X = 0)) (0 orange spins)

The outcome with 0 orange spins is GGG. So (P(X = 0)=\frac{1}{8}=0.125).

Step3: Calculate (P(X = 1)) (1 orange spin)

The outcomes with 1 orange spin are GGO, GOG, OGG. So (P(X = 1)=\frac{3}{8}=0.375).

Step4: Calculate (P(X = 2)) (2 orange spins)

The outcomes with 2 orange spins are GOO, OGO, OOG. So (P(X = 2)=\frac{3}{8}=0.375).

Step5: Calculate (P(X = 3)) (3 orange spins)

The outcome with 3 orange spins is OOO. So (P(X = 3)=\frac{1}{8}=0.125).

The probability distribution has values (P(X = 0)=0.125), (P(X = 1)=0.375), (P(X = 2)=0.375), (P(X = 3)=0.125). We would need to compare these values with the given graphs to determine the correct one. But based on the calculations, the bar - heights for (x = 0) and (x = 3) should be the same (0.125) and the bar - heights for (x = 1) and (x = 2) should be the same (0.375).

Since the graphs are not fully described in text, we assume the correct graph has bars at (x = 0) with height 0.125, at (x = 1) with height 0.375, at (x = 2) with height 0.375 and at (x = 3) with height 0.125.

Answer:

The graph with bar - heights 0.125 at (x = 0) and (x = 3), and bar - heights 0.375 at (x = 1) and (x = 2).