Question 9 • Concepts in Probability and Statistics
Veronique has a spinner with three sections of equal size, red r , green g , and blue b The spinner is spun twice. The sample space for the possible outcomes is cap s is equal to rr, rb, rg, gr, gg, gb, br, bg, bb If the number of times red is spun is the random variable, cap x , which graph represents the probability distribution?
Answer
A
Image with description Bar graph titled “Probability Distribution.” The horizontal axis, labeled X, shows the outcomes “0 times,” “1 time,” and “2 times.” The vertical axis, labeled P subscript X of x, ranges from 0 to 0.6 with tick marks at intervals of 0.1. Three bars are displayed. The bar for “0 times” has height 0.5, the bar for “1 time” has height approximately 0.35, and the bar for “2 times” has height approximately 0.15. The graph shows that the probability decreases as the number of occurrences increases.
B
Image with description Bar graph titled “Probability Distribution.” The horizontal axis, labeled X, shows three outcomes: “0 times,” “1 time,” and “2 times.” The vertical axis, labeled Pₓ(x), ranges from 0 to 0.4 with tick marks at 0.1 intervals. Three bars are shown, one above each outcome, and all three bars have the same height, approximately 0.33 (one-third). This indicates that the probabilities of X being 0, 1, or 2 are equal.
C
Image with description The bar graph entitled Probability Distribution represents the probability of how many times the color red is spun as a random variable. The x axis shows the possible values of the variable X, from 0 times to 1 time and 2 times, while the y axis shows the probability ranging from 0 to 0 point 6, in increments of 0.1, labeled as P subscript x of x. There are 3 bars. The first bar is at 0 times and its height is 0 point 55, the second bar is at 1 time and its height is 0 point 32, and the third bar is at 2 times and its height is 0 point 11.
D
Image with description Bar graph titled “Probability Distribution.” The horizontal axis, labeled X, shows three outcomes: “0 times,” “1 time,” and “2 times.” The vertical axis, labeled Pₓ(x), ranges from 0 to 0.4 with tick marks at 0.1 intervals. Three bars are shown, one above each outcome, and all three bars have the same height, approximately 0.33 (one-third). This indicates that the probabilities of X being 0, 1, or 2 are equal.