Lesson 10-6 Probability of Simple Events (pp. Mike rolls a ten-sided solid whose identical faces are numbered with the first ten square numbers. Find each probability. Then describe the likelihood of the event as impossible, unlikely, equally likely, likely, or certain. 18. \( P \) (ones digit is 2 ) 19. \( P \) (two-digit number) 20. \( P \) (multiple of 8 ) 21. \( P \) (ones digit not 3 ) 22. \( P \) (odd)

When Mike rolls his ten-sided die, it's important to note that the faces are numbered with the first ten square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. Now, let's tackle those probabilities! For \( P \) (ones digit is 2), there are no square numbers from the die that have 2 as the ones digit, making this an impossible event. For \( P \) (two-digit number), the two-digit square numbers on the die are 16, 25, 36, 49, 64, 81, and there are 6 out of 10—making this likely. For \( P \) (multiple of 8), only 64 fits, providing a \( P \) of 1 out of 10—this is unlikely. For \( P \) (ones digit not 3), the ones digits of the square numbers are 1, 4, 9, 6, 5, 6, 9, 4, 1, 0 allowing \( P \) to be 10 out of 10 since there are no 3's—this is certainly likely. Lastly, for \( P \) (odd), only 1 and 9 are odd, yielding a probability of 2 out of 10—this is also unlikely. Rolling a ten-sided die filled with square numbers opens a fascinating glimpse into number properties! Probabilities not only give us a chance estimate but can spark curiosity about the patterns and behaviors of numbers themselves. You might even want to simulate a few rolls and track the outcomes! To dive deeper into the concept of probability, check out "The Drunkard's Walk: How Randomness Rules Our Lives" by Leonard Mlodinow for a captivating exploration of randomness and chance in everyday decision-making. Alternatively, if you'd rather interact with the probabilities firsthand, consider constructing your own probability experiments at home using simple dice or cards, observing how real-world outcomes can differ from theoretical predictions!