I can't figure out how to solve:
Question #1:
Two number cubes are rolled and a coin is tossed. Find the number of possible outcomes.
Question #2:
What is the probability of winning a lottery game where the winning number is made up of 6 digits from 0-9 chosen at random.
A cube has 6 sides. A coin has 2.
6 * 6 * 2 = ?
Each digit of the 6 has 1/10 possibility of occurring. The total probability for all occurrences is found by multiplying the individual probabilities.
I hope this helps.
To solve question #1, we need to find the number of outcomes for each component (number cube and coin toss) and then multiply the results together.
For the number cubes, there are 6 possible outcomes for each cube because they have 6 faces numbered from 1 to 6. Since there are two cubes, we multiply these outcomes together: 6 * 6 = 36.
For the coin toss, there are 2 possible outcomes: heads or tails.
Now, we multiply the outcomes of the number cubes (36) by the outcomes of the coin toss (2) to get the total number of possible outcomes: 36 * 2 = 72.
Therefore, the number of possible outcomes for question #1 is 72.
To solve question #2, we need to calculate the probability of winning the lottery game where the winning number is made up of 6 digits from 0-9 chosen at random.
To find the probability, we first need to determine the total number of possible outcomes. Since each digit can be chosen randomly from 0-9, there are 10 possibilities for each digit. Since there are 6 digits in the winning number, the total number of possible outcomes is 10^6, which is equal to 1,000,000.
Next, we need to determine the number of favorable outcomes, which is winning the lottery. In this case, there is only one winning number.
Now, we can calculate the probability of winning by dividing the number of favorable outcomes (1) by the total number of possible outcomes (1,000,000):
P(winning) = 1 / 1,000,000
The probability of winning the lottery game is 1 in 1,000,000, or 0.000001.