A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 2 and the coin toss is tails?
Write your answer as a fraction in simplest form.
To find the probability of two independent events occurring, you multiply their individual probabilities.
Let's start with the number cube. A number cube has six faces, so there are a total of 6 possible outcomes. Since the number cube is fair, each outcome has an equal chance of occurring.
The probability of rolling a number greater than 2 is 4/6, because there are 4 favorable outcomes (3, 4, 5, and 6) out of 6 total outcomes.
Now let's move to the coin toss. A coin has two sides, so there are 2 possible outcomes, heads or tails. Since the coin is fair, each outcome has an equal chance of occurring.
The probability of getting tails is 1/2, because there is 1 favorable outcome (tails) out of 2 total outcomes.
To find the probability of both events occurring, you multiply the individual probabilities:
Probability of rolling a number greater than 2 and getting tails = (4/6) * (1/2) = 4/12 = 1/3
Therefore, the probability that the number rolled is greater than 2 and the coin toss is tails is 1/3.
To find the probability that the number rolled is greater than 2 and the coin toss is tails, we need to determine the probability of each event separately and then multiply them together.
The number cube has 6 sides, numbered 1 to 6. Since it is fair, each number has an equal chance of being rolled. There are four numbers greater than 2: 3, 4, 5, and 6. So, the probability of rolling a number greater than 2 is 4/6 or 2/3.
The coin has 2 sides, heads and tails. Both sides have an equal chance of occurring. So, the probability of tossing tails is 1/2.
Now, we can multiply these probabilities together to find the combined probability:
Probability = Probability of rolling a number > 2 × Probability of tossing tails
Probability = (2/3) × (1/2)
Probability = 2/6
Probability = 1/3
Therefore, the probability that the number rolled is greater than 2 and the coin toss is tails is 1/3.
There are two events that we need to consider here: rolling a number cube and tossing a coin. Both events are independent of each other, meaning the outcome of one does not affect the outcome of the other.
The probability of rolling a number greater than 2 is 4/6 or 2/3, since there are four numbers on a standard number cube that are greater than 2.
The probability of tossing tails on a fair coin is 1/2.
To find the probability of both events happening together, we multiply their probabilities:
2/3 x 1/2 = 1/3
Therefore, the probability of rolling a number greater than 2 and tossing tails is 1/3.