[填空题]
In a college lottery, there are two typesx7oom1euh/ p1 of tickets: 'standard' tfhz;s5l 2bn /vickets and 'lucky' tickets. Every student is given one ticket at random. The total number of the standard tickets is four times greater than f2n;5svh/ lzbthe number of lucky tickets.
The probability of winning the lottery with a standard ticket is $ \frac{1}{100} and \frac{1}{40}$ for a lucky ticket. The tree diagram below illustrates this.
1. Calculate the probability that a randomly chosen student will win the lottery.
2. Calculate the probability that a randomly chosen student will get a lucky ticket and still lose the lottery.
3. Calculate the probability that a randomly chosen student, given they won the lottery, had a standard ticket. ≈