A fair coin has 2 sides : 1 side is heads and 1 side is tails. A fair cube has 6 sides: 2 sides are solid green, 2 sides are solid yellow, and 2 sides are solid red. The coin and the cube are each tossed once. What is the probability they will land so that the side facing up on the coin is tails and the side facing up on the cube is yellow?
Question
A fair coin has 2 sides : 1 side is heads and 1 side is tails. A fair cube has 6 sides: 2 sides are solid green, 2 sides are solid yellow, and 2 sides are solid red. The coin and the cube are each tossed once. What is the probability they will land so that the side facing up on the coin is tails and the side facing up on the cube is yellow?
Solution
To solve this problem, we need to multiply the probability of each independent event.
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The probability of the coin landing on tails: Since a fair coin has 2 sides (heads and tails), the probability of it landing on tails is 1/2.
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The probability of the cube landing on yellow: The cube has 6 sides, 2 of which are yellow. So, the probability of it landing on yellow is 2/6, which simplifies to 1/3.
Now, we multiply these two probabilities together to get the overall probability of both events happening at the same time.
(1/2) * (1/3) = 1/6
So, the probability that the coin will land on tails and the cube will land on yellow is 1/6.
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