You roll two number cubes and you spin a spinner with 10 colors and numbers 0-16. You win the game if you roll two odd numbers followed by an odd number on the spinner. If you spin once, what is the chance you will win the game?
I assume you only roll the cubes once.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
1/2 * 1/2 * 8/17 = ?
To find the chance of winning the game, we first need to determine the total number of possible outcomes and the number of successful outcomes.
First, let's determine the number of possible outcomes for rolling two number cubes and spinning the spinner.
For rolling two number cubes, each cube has 6 faces numbered from 1 to 6. Since there are two cubes, there are 6 * 6 = 36 possible outcomes for rolling the number cubes.
For spinning the spinner, there are 10 colors and numbers from 0-16. That means there are a total of 10 + 17 = 27 possible outcomes for spinning the spinner.
To calculate the total number of possible outcomes, we multiply the number of outcomes for rolling the number cubes (36) by the number of outcomes for spinning the spinner (27), which gives us 36 * 27 = 972 total possible outcomes.
Now, let's determine the number of successful outcomes, which in this case, is rolling two odd numbers followed by an odd number on the spinner.
For the first roll of the number cubes, we need an odd number, which is 1, 3, or 5. Therefore, there are 3 possible outcomes.
For the second roll of the number cubes, we still need an odd number, and again there are 3 possible outcomes.
Finally, for spinning the spinner, we need an odd number, which can be 1, 3, 5, 7, 9, 11, 13, or 15. Therefore, there are 8 possible outcomes.
To calculate the number of successful outcomes, we multiply the number of outcomes for each step together: 3 * 3 * 8 = 72 successful outcomes.
Now that we know the number of possible outcomes (972) and the number of successful outcomes (72), we can find the chance of winning the game by dividing the number of successful outcomes by the number of possible outcomes:
Chance of winning = (Number of successful outcomes / Number of possible outcomes) * 100
= (72 / 972) * 100
= 7.4%
Therefore, the chance of winning the game is approximately 7.4%.