It you roll two dice find the number of outcomes for each of the following events:
A)rolling two prime numbers
B) rolling at least one odd number
A) i got 9 outcomes
B) i got 27 outcomes
i used a table to figure this out are my solutions correct?
To verify your solutions, let's go through the process of finding the number of outcomes for each event.
Event A) rolling two prime numbers:
The prime numbers between 1 and 6 (the numbers on a die) are 2, 3, and 5.
To find the number of outcomes with two prime numbers, we need to count the number of favorable outcomes. There are three options for the first die roll (2, 3, and 5), and similarly, there are three options for the second die roll.
Using the fundamental counting principle, which states that if you have m choices for one event and n choices for another event, then you have m x n choices for the combination of those events, we can multiply the number of options for each die roll.
So, for event A, the number of outcomes would be 3 (options for the first die roll) x 3 (options for the second die roll) = 9 outcomes.
Therefore, your solution of 9 outcomes for event A is correct.
Event B) rolling at least one odd number:
To find the number of outcomes where at least one die roll is odd, we need to consider the complementary event, where both die rolls are even.
The even numbers between 1 and 6 (the numbers on a die) are 2, 4, and 6.
To determine the number of outcomes where both die rolls are even, we use the same process as in event A. There are three options for the first die roll and three options for the second die roll.
Using the fundamental counting principle, the number of outcomes for both die rolls being even would be 3 (options for the first die roll) x 3 (options for the second die roll) = 9 outcomes.
However, we are interested in the complementary event, where at least one die roll is odd. Therefore, we need to subtract the number of outcomes where both die rolls are even from the total number of possible outcomes (36 outcomes in total for two dice).
Total number of outcomes - Number of outcomes with both even rolls = 36 - 9 = 27 outcomes.
Thus, your solution of 27 outcomes for event B is also correct.
In conclusion, your solutions are correct for both events A and B.