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Jacci has a fair coin and a wooden cube. On the cube, there are two faces colored green, two faces colored blue, and two faces colored red. Mary flips the coin and tosses the cube. What is the probability of getting both a tail on the toss of the coin and a green face on the roll of the cube?

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Find probabilities using the addition rule

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Q. Jacci has a fair coin and a wooden cube. On the cube, there are two faces colored green, two faces colored blue, and two faces colored red. Mary flips the coin and tosses the cube. What is the probability of getting both a tail on the toss of the coin and a green face on the roll of the cube?

Determine Probability of Tail: Determine the probability of getting a tail on the toss of the coin. $\newline$ Since a fair coin has two sides, heads and tails, the probability of getting a tail is $1$ out of $2$ . $\newline$ Probability of getting a tail $= \frac{1}{2}$
Determine Probability of Green Face: Determine the probability of getting a green face on the roll of the cube. The cube has $6$ faces, with $2$ of them being green. Therefore, the probability of rolling a green face is $2$ out of $6$ . Probability of getting a green face $= \frac{2}{6}$ However, $\frac{2}{6}$ can be simplified to $\frac{1}{3}$ .
Calculate Combined Probability: Calculate the combined probability of both events happening together. $\newline$ Since the coin flip and the cube roll are independent events, the combined probability is the product of the probabilities of each individual event. $\newline$ Combined probability = Probability of getting a tail $\times$ Probability of getting a green face $\newline$ Combined probability = $(\frac{1}{2}) \times (\frac{1}{3})$
Perform Multiplication: Perform the multiplication to find the combined probability. Combined probability = $(\frac{1}{2}) \times (\frac{1}{3}) = \frac{1}{6}$

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