Jasim has seven cards numbered 2 to 8 Jasim takes at random three of these cards. He works out the sum of the numbers on the three cards and records the result. Work out the probability that the result is an odd number. Optional working

To determine the probability that Jasim's sum of the three cards he randomly selects results in an odd number, we first need to know how the sum of numbers can be odd. A sum of three numbers is odd if either one of the numbers is odd and the other two are even, or all three numbers are odd. In Jasim's set of cards (2, 3, 4, 5, 6, 7, 8), we have four even numbers (2, 4, 6, 8) and three odd numbers (3, 5, 7). To achieve an odd sum, the following combinations are possible: 1. One odd and two evens 2. Three odds (which is not possible since there are only three odd numbers and selecting three would be an odd count). Let’s calculate the scenarios: - For one odd and two evens: The number of ways to select one odd from the three odd cards is \( \binom{3}{1} \) and the number of ways to select two evens from the four even cards is \( \binom{4}{2} \). Calculating these gives: - \( \binom{3}{1} = 3 \) (choosing 1 from 3 odd numbers) - \( \binom{4}{2} = 6 \) (choosing 2 from 4 even numbers) Thus, the total combinations resulting in an odd sum are: \( 3 \times 6 = 18 \). The total possible combinations of choosing any three cards from seven is given by \( \binom{7}{3} = 35 \). Finally, the probability is given by: \[ P(\text{odd sum}) = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{18}{35}. \] Now for the engaging extra bits: Want to dive deeper into probability? Did you know that probability is not just a math topic, but it’s widely used in fields such as insurance, finance, and even game design? Gamblers rely on it every day when they calculate their odds, whether in poker or when playing roulette. To round out your knowledge, if you enjoyed the puzzles of probability, there are plenty of awesome books out there! “The Drunkard's Walk: How Randomness Rules Our Lives” by Leonard Mlodinow is a fantastic read that makes the subject approachable while explaining how random events shape our daily lives.