Question

A gumball machine gives out a red, a black, or a green ball. a. State the appropriate sample space. b. List all possible events c. If R is the event with element "red", then list the outcomes in R d. If G is the event "green", then what is RnG?.

Answer 1

The appropriate sample space for the gumball machine is {red, black, green}. The possible events include the individual colors, combinations of two colors, and the empty set. The outcomes in the event R, which represents the red ball, are {red}. The event R ∩ G, or the intersection of events R and G, consists of the outcomes where both a red and a green ball are chosen.

Step-by-step explanation:

a. The appropriate sample space for the gumball machine is {red, black, green}.

b. The possible events are: {red}, {black}, {green}, {red, black}, {red, green}, {black, green}, {red, black, green}, and the empty set {}.

c. The outcomes in the event R, which represents the red ball, are {red}.

d. The intersection of events R and G, denoted as R ∩ G, is the event {red, green}, which consists of the outcomes where both a red and a green ball are chosen.

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