(Unit 2 Lesson 7)
A coin is tossed, and a standard number cube is rolled. What is the probablility that the coin shows heads and the cube shows an even number?
To find the probability that a coin shows heads and a standard number cube shows an even number, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Let's start by counting the number of total outcomes. Since there are two possible outcomes when flipping a coin (heads or tails) and six possible outcomes when rolling a standard number cube (numbers 1 through 6), the total number of outcomes is: 2 (coin outcomes) × 6 (number cube outcomes) = 12.
Next, let's determine the number of favorable outcomes. We want the coin to show heads and the cube to show an even number. Since there is only one favorable outcome when flipping a coin (heads) and three favorable outcomes when rolling a standard number cube (even numbers 2, 4, and 6), the number of favorable outcomes is: 1 (coin outcome) × 3 (number cube outcomes) = 3.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes: probability = number of favorable outcomes / total number of outcomes = 3 / 12 = 1/4.
Therefore, the probability that the coin shows heads and the cube shows an even number is 1/4 or 25%.