Question

calculating probability from a frequency table

the fair spinner shown is spun 2 times. the set of possible outcomes are:

\\(s = \\{rr, bb, yy, gg, rb, br, ry, yr, rg, gr, by, yb, bg, gb, yg, gy\\}\\)

the number of yellows in the outcome is summarized in the table on the right.

using the data from the theoretical probability table, what is the probability of the spinner landing only once on yellow in two spins?

• 0.0625
• 0.5625
• 0.375
• 1

Explanation:

Sum the frequencies to find the total outcomes

Using the Experimental Probability knowledge point

$$ \text{Total Frequency} = 9 + 6 + 1 = 16 $$

Identify the frequency of landing exactly once on yellow

Using the Experimental Probability knowledge point

$$ \text{Frequency of 1 Yellow} = 6 $$

Calculate the probability of landing only once on yellow

Using the Theoretical Probability knowledge point

$$ P(\text{exactly 1 yellow}) = \frac{6}{16} = 0.375 $$

Answer:

• 0.0625
• 0.5625
• 0.375 (Correct answer)
• 1