There are two integers from 1 through 40 and are chosen by a random number generator.
Write the final answer in a/b form.
1.) P(the same number is chosen twice)
2.) P(both numbers are less than 30)
3.) P(one number is even and one number is odd)
4.) P(both numbers are even)
1/40^2
2) 3/4 ^2
3) pr(even or odd)*pr(odd or even)
1/2
note the pr first is odd, secnd is even is 1/4, but the pr first id even, second is odd is 1/4, adding them, 1/2
4) 1/2*1/2
SO, would I have to square #1 and 2 to get my answer?
yes.
a) 1/40 * 1/40
So, would #2 be 6/4=3/2?
3/4 times 3/4 is 9/16
And that's in the simplest form?
To find the answers to each of the probability questions, we need to determine the number of favorable outcomes and the total number of possible outcomes. We can then calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
1.) P(the same number is chosen twice)
To calculate this probability, we need to determine the number of ways we can choose the same number twice. Since there are 40 integers to choose from, there are 40 favorable outcomes. The total number of possible outcomes is also 40, as we can choose any number from 1 to 40 twice. Therefore, the probability is 40/40, which simplifies to 1.
2.) P(both numbers are less than 30)
In this case, we are interested in finding the number of ways we can choose two numbers less than 30. There are 29 integers from 1 through 29 that are less than 30, so the number of favorable outcomes is 29 * 29 = 841. The total number of possible outcomes is 40 * 40 = 1600. Therefore, the probability is 841/1600.
3.) P(one number is even and one number is odd)
To calculate this probability, we need to consider the number of ways we can select one even number and one odd number. There are 20 even numbers (2, 4, 6, ..., 40) and 20 odd numbers (1, 3, 5, ..., 39). Therefore, the number of favorable outcomes is 20 * 20 = 400. The total number of possible outcomes is 40 * 40 = 1600. Therefore, the probability is 400/1600, or 1/4.
4.) P(both numbers are even)
In this case, we are interested in finding the number of ways we can choose two even numbers. Since there are 20 even numbers to choose from, the number of favorable outcomes is 20 * 20 = 400. The total number of possible outcomes is 40 * 40 = 1600. Therefore, the probability is 400/1600, or 1/4.
So, the final answers are:
1.) 1
2.) 841/1600
3.) 1/4
4.) 1/4