Question

A computer is used to generate ten random integers, each between 0 and 9 (with replacement). Let X equal the number of even numbers among the ten numbers picked. That is, if the ten random integers turn out to be 1324555779 , then X=2. (a) Find the probability that one of the random integers is even. (b) Find the probability that seven or fewer even numbers are picked among the ten random integers.

Answer 1

The probability that one of the random integers is even is 0.5. The probability that seven or fewer even numbers are picked among the ten random integers can be calculated by summing up the probabilities of picking different numbers of even numbers.

Step-by-step explanation:

To find the probability that one of the random integers is even, we need to find the probability of selecting an even number from the range of 0 to 9. There are a total of 10 numbers in this range, and 5 of them are even (0, 2, 4, 6, 8). So, the probability is 5/10 or 0.5.

To find the probability that seven or fewer even numbers are picked among the ten random integers, we can calculate the probability of picking 0, 1, 2, 3, 4, 5, 6, or 7 even numbers and sum them up. The probability of picking 0 even numbers is (5/10)^10. The probability of picking 1 even number is 10C1 (number of ways to choose 1 even number) times (5/10)^1 times (5/10)^9. Similarly, we can calculate the probabilities for picking 2, 3, 4, 5, 6, and 7 even numbers and sum them up to get the total probability.