Final answer:
The probability of winning on the fourth scratch-off lottery ticket, given a 20 percent chance of winning on any ticket, is 10.24 percent after multiplying the probabilities of losing the first three tickets and winning the fourth.
Step-by-step explanation:
The question is asking for the probability of a person winning on the fourth scratch-off lottery ticket, given a 20 percent chance of winning on any given ticket. To find this, we need to calculate the probability of the person not winning on the first three tickets and then winning on the fourth ticket. The probability of not winning on a single ticket is 1 - 0.20 = 0.80 (or 80 percent). The events are independent, so we multiply the probabilities together:
- Probability of losing the first ticket = 0.80
- Probability of losing the second ticket = 0.80
- Probability of losing the third ticket = 0.80
- Probability of winning on the fourth ticket = 0.20
The combined probability of these four independent events occurring in sequence is 0.80 × 0.80 × 0.80 × 0.20, which equals 0.1024 or 10.24 percent when rounded to four decimal places as requested.