[填空题]
In a college lottery, thu6obb1 (zk v8xere are two ,xp 5-pams- vhm44ncntypes of tickets: 'standard' tickets and 'lucky' tickets. Every student xc4 mh4s pmvn np5a,--is given one ticket at random. The total number of the standard tickets is four times greater than the 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. ≈