Two numbers are chosen from 1 to 20Find the probability

Solution

ATQ, To find the probability that two numbers chosen from 1 to 20 are consecutive, you can use the following approach: Step 1: Determine the total number of ways to choose any two numbers from 1 to 20. This is done by calculating combinations. Total Ways to Choose 2 Numbers = C(20, 2) C(20, 2) = (20!)/[2!(20-2)!] = (20 × 19)/(2 × 1) = 190 ways Step 2: Determine the number of ways to choose two consecutive numbers from 1 to 20. Since consecutive numbers can start from 1 and go up to 19 (as 20 doesn't have a consecutive number following it),then Number of Ways to Choose Consecutive Numbers = 19ways Step 3: Calculate the probability: Probability (Choosing Consecutive Numbers) = (Number of Ways to Choose Consecutive Numbers) / (Total Ways to Choose 2 Numbers) Probability (Choosing Consecutive Numbers) = 19/190 Now, simplify the fraction if necessary: Probability (Choosing Consecutive Numbers) = 1/10 So, the probability that two numbers chosen from 1 to 20 are consecutive is 1/10 or 10% or 0.1