a coin is tossed and a number cube is rolled what is the probability that the coin shows heads and the number cube shows an even number
Assuming the coin is fair (has an equal chance of landing on heads or tails) and the number cube is also fair (has an equal chance of rolling any of its six sides), we can determine the probability of both events happening by multiplying their probabilities.
The probability of the coin showing heads is 1/2 (or 0.5), since there are two equally likely outcomes (heads or tails) and one of them is heads.
The probability of the number cube showing an even number is 3/6, or 1/2, since there are three even numbers (2, 4, and 6) out of six possible outcomes.
To find the probability of both events happening (the coin showing heads and the number cube showing an even number), we multiply their probabilities:
1/2 x 1/2 = 1/4
So the probability of both events happening is 1/4, or 0.25.
To find the probability that the coin shows heads and the number cube shows an even number, we need to determine the number of favorable outcomes and the total number of possible outcomes.
For the coin, there are 2 possible outcomes: heads (H) or tails (T).
For the number cube, there are 6 possible outcomes: 1, 2, 3, 4, 5, or 6.
To find the favorable outcomes, we need to find the intersection of having heads and an even number. In this case, the favorable outcomes are H2 (heads and a 2), H4 (heads and a 4), H6 (heads and a 6).
Therefore, the probability of getting heads and an even number = Number of favorable outcomes / Total number of possible outcomes
So, there are 3 favorable outcomes and a total of (2 * 6) = 12 possible outcomes.
Hence, the probability is 3/12, which simplifies to 1/4 or 0.25.