This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Welcome back — been a while! Let's pick up where you left off. Step 1: Determine the total number of possible outcomes. The box contains 90 discs numbered from 1 to 90. Total number of outcomes = 90. i) Find the probability that the disc bears a two-digit number. Step 2: Identify the number of two-digit numbers. The numbers from 1 to 90 include one-digit numbers (1 to 9) and two-digit numbers (10 to 90). Number of one-digit numbers = 9. Number of two-digit numbers = Total numbers - Number of one-digit numbers Number of two-digit numbers = 90 - 9 = 81. Step 3: Calculate the probability of drawing a two-digit number. P(two-digit number) = Number of two-digit numbersTotal number of discs P(two-digit number) = (81)/(90) P(two-digit number) = (9)/(10) The probability of drawing a two-digit number is (9)/(10). ii) Find the probability that the disc bears a perfect square number. Step 4: Identify the perfect square numbers between 1 and 90. Perfect squares are numbers that can be expressed as n^2. The perfect squares are: 1^2 = 1 2^2 = 4 3^2 = 9 4^2 = 16 5^2 = 25 6^2 = 36 7^2 = 49 8^2 = 64 9^2 = 81 (10^2 = 100, which is greater than 90, so it's not included). Number of perfect square numbers = 9. Step 5: Calculate the probability of drawing a perfect square number. P(perfect square number) = Number of perfect square numbersTotal number of discs P(perfect square number) = (9)/(90) P(perfect square number) = (1)/(10) The probability of drawing a perfect square number is (1)/(10). iii) Find the probability that the disc bears a number divisible by 5. Step 6: Identify the numbers divisible by 5 between 1 and 90. These are 5, 10, 15, ..., 90. To find the count, divide the last number by 5: Number of numbers divisible by 5 = (90)/(5) = 18. Step 7: Calculate the probability of drawing a number divisible by 5. P(number divisible by 5) = Number of numbers divisible by 5Total number of discs P(number divisible by 5) = (18)/(90) P(number divisible by 5) = (1)/(5) The probability of drawing a number divisible by 5 is (1)/(5). Send me the next one 📸