1. When two fair dice are tossed, what is the probability of a sum of 4 or a sum of 8?
2. When two fair dice are tossed, what is the probability of doubles or a sum over 9?
3. Evaluate 1025! / 1022!
Please help
1. You cant get 14 with two regular six-sided dice. The highest you can get with one throw is 12 so the probability would be 0
sorry i only can figure out #1 right now, if i figure all of it out then i will let you know.
Sorry i messed up, what i meant was:
1. 8/36
2. Use the similar process
3. 1023*1024*1025= 1073740800 1.0737408 x 10*9
1. To find the probability of getting a sum of 4 or a sum of 8 when two fair dice are tossed, we need to determine the number of favorable outcomes and the total number of possible outcomes.
For the sum of 4, there are three favorable outcomes: (1, 3), (2, 2), and (3, 1).
For the sum of 8, there are five favorable outcomes: (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2).
Therefore, there are a total of 3 + 5 = 8 favorable outcomes.
To find the total number of possible outcomes, we multiply the number of outcomes for each die. Since each die can have 6 outcomes (numbers from 1 to 6), there are 6 × 6 = 36 possible outcomes when two dice are rolled.
Therefore, the probability of getting a sum of 4 or a sum of 8 is 8/36, which simplifies to 2/9.
2. To find the probability of getting doubles or a sum over 9 when two fair dice are tossed, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
For doubles, there are six favorable outcomes: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6).
For a sum over 9, we have the following favorable outcomes: (4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6).
Therefore, there are a total of 6 + 6 = 12 favorable outcomes.
To find the total number of possible outcomes, we multiply the number of outcomes for each die, which is 6 × 6 = 36 possible outcomes when two dice are rolled.
Therefore, the probability of getting doubles or a sum over 9 is 12/36, which simplifies to 1/3.
3. To evaluate 1025! / 1022!, we first need to understand factorial notation. Factorial of a number n, denoted by n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
In this case, we have 1025! in the numerator and 1022! in the denominator. To simplify this expression, we can cancel out the common terms.
The terms canceled out are 1025 × 1024 × 1023, leaving us with 1025! / 1022! = 1025 × 1024 × 1023.
So, the simplified value of 1025! / 1022! is 1025 × 1024 × 1023.