Question

two integers are selected at random from integers 1 through 16 after replacing the first integer. find the probability that the first number is even and second number is odd

Answer 1

The probability that the first number selected is even and the second number is odd from the integers 1 through 16 is 1/4 or 25%.

Step-by-step explanation:

The question asks for the probability that the first number chosen is even and the second number chosen is odd, given that the selection is made from the integers 1 through 16.

First, let's determine the total number of even and odd numbers in the given range:

• There are 8 even numbers (2, 4, 6, 8, 10, 12, 14, 16).
• There are also 8 odd numbers (1, 3, 5, 7, 9, 11, 13, 15).

Since the first integer is replaced before selecting the second, the total number of possible outcomes for each selection is 16. The events are independent.

To calculate the probability:

1. Find the probability of selecting an even number first (event A): P(A) = number of even numbers / total numbers = 8/16 = 1/2.
2. Find the probability of selecting an odd number second (event B): P(B) = number of odd numbers / total numbers = 8/16 = 1/2.
3. Since the events are independent, multiply the probabilities of A and B: P(A and B) = P(A) x P(B) = (1/2) x (1/2) = 1/4.

Therefore, the probability that the first number is even and the second number is odd is 1/4 or 25%.