Assume that 3 dice are thrown simultaneously. What is the probability that exactly one 4 will come up?
There are six sides on each dice. Each dice has 1 four.
There are 3 fours for the three dice.
There are a total of 18 possibilities of outcomes.
So, you have 4/18 = 2/9.
To find the probability of exactly one 4 coming up when three dice are thrown simultaneously, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
Let's start by calculating the total number of possible outcomes. When throwing three dice, each die has 6 possible outcomes (numbers 1 to 6). Since we are throwing three dice simultaneously, the total number of possible outcomes is 6 * 6 * 6 = 216.
Next, let's calculate the number of favorable outcomes, which is the number of outcomes where exactly one 4 comes up. There are three different ways this can happen:
1. The first die shows a 4, and the other two show any other number: This can occur in 1 * 5 * 5 = 25 ways.
2. The second die shows a 4, and the other two show any other number: This can occur in 5 * 1 * 5 = 25 ways.
3. The third die shows a 4, and the other two show any other number: This can occur in 5 * 5 * 1 = 25 ways.
Since these three ways are mutually exclusive (they cannot happen at the same time), we can add up the number of favorable outcomes: 25 + 25 + 25 = 75.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
Probability = 75 / 216
Simplifying this fraction, we get:
Probability ≈ 0.3472
Therefore, the probability that exactly one 4 will come up when three dice are thrown simultaneously is approximately 0.3472, or 34.72%.