Problem
August U Johnson Chapter 11 Test Numbers from Sets of Digits Two numbers are randomly selected without replacement from the set $\{1,2,3,4,5\}$. Find the probability of each event. 1. Both numbers are even. 2. Both numbers are prime 3. The sum of the two numbers is odd. 4. The product of the two numbers is odd. Days Off for Pizza Parlor Workers The manager of a pizza parlor (which operates seven days a week) allows each of three employees to select one day off next week. Assuming the selection is done randomly and independently, find the probability of each event. 5. All three select different days. 6. All three select the same day, given that all three select a day beginning with the same letter.
Solution
Step 1 ：Calculate the probability for each event using combinations.
Step 2 ：1. Both numbers are even: \(0.1\)
Step 3 ：2. Both numbers are prime: \(0.3\)
Step 4 ：3. The sum of the two numbers is odd: \(0.6\)
Step 5 ：4. The product of the two numbers is odd: \(0.3\)
Step 6 ：5. All three select different days: \(0.10204081632653061\)
Step 7 ：6. All three select the same day, given that all three select a day beginning with the same letter: \(0.5\)
Step 8 ：\(\boxed{\text{Final Answer:}}\)
Step 9 ：1. \(\boxed{0.1}\)
Step 10 ：2. \(\boxed{0.3}\)
Step 11 ：3. \(\boxed{0.6}\)
Step 12 ：4. \(\boxed{0.3}\)
Step 13 ：5. \(\boxed{0.10204081632653061}\)
Step 14 ：6. \(\boxed{0.5}\)
