Lottery: Every day, Jorge buys a lottery ticket. Each ticket has a probability of 0.4 of winning a prize. After five days, what is the probability that Jorge has won at least one prize? Round your answer to four decimal places.

To find the probability that Jorge has won at least one prize after five days, we can use the complement rule. First, we will calculate the probability that he does not win any prizes in those five days, and then subtract that from 1. 1. The probability of winning a prize on a single ticket is \( p = 0.4 \). 2. Therefore, the probability of not winning a prize on a single ticket is \( 1 - p = 1 - 0.4 = 0.6 \). 3. The probability of not winning any prizes over five days (i.e., buying five tickets) is: \[ (0.6)^5 \] 4. Now we calculate \( (0.6)^5 \): \[ (0.6)^5 = 0.07776 \] 5. The probability of winning at least one prize in five days is: \[ 1 - (0.6)^5 = 1 - 0.07776 = 0.92224 \] 6. Finally, rounding to four decimal places, we get: \[ \text{Probability of winning at least one prize} \approx 0.9222 \] Thus, the probability that Jorge has won at least one prize after five days is **0.9222**.