Daily Math Puzzle: 2026-10-25

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2026-10-25

At your favorite grocery store, for every purchase over $50, you receive a 'Lucky Scratch' ticket. These tickets have a 1 in 5 chance of winning a $10 store voucher and a 1 in 20 chance of winning a $50 store voucher. All other tickets are losing tickets (winning $0). You make two separate purchases over $50 on the same day, so you get two Lucky Scratch tickets. What is the probability that you win at least $10 in total from your two tickets?

1/41/27/169/16

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Solution

7/16 — Let's define the probabilities for a single Lucky Scratch ticket: - Probability of winning a $10 voucher (P($10)) = 1/5 - Probability of winning a $50 voucher (P($50)) = 1/20 - Probability of winning $0 (Losing, P($0)) = 1 - P($10) - P($50) First, calculate the probability of a losing ticket: P($0) = 1 - (1/5) - (1/20) P($0) = 1 - (4/20) - (1/20) P($0) = 1 - 5/20 P($0) = 1 - 1/4 P($0) = 3/4 You get two Lucky Scratch tickets, and the outcomes are independent. We want to find the probability that you win at least $10 in total. It's often easier to calculate the probability of the complementary event and subtract it from 1. The complementary event is winning 'less than $10' in total. The only way to win less than $10 in total from two tickets is if both tickets are losing tickets (i.e., you win $0 from the first ticket AND $0 from the second ticket). Probability of winning less than $10 total = P(Ticket 1 is $0) * P(Ticket 2 is $0) Probability of winning less than $10 total = (3/4) * (3/4) Probability of winning less than $10 total = 9/16 Now, subtract this from 1 to find the probability of winning at least $10 in total: Probability of winning at least $10 total = 1 - P(winning less than $10 total) Probability of winning at least $10 total = 1 - 9/16 Probability of winning at least $10 total = 7/16

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