And become the governor, and fly to the moon

Several tasks of Medusa about interest and elections. No miracles!

When counting the votes in the election of the governor of Primorye, a mathematical miracle occurred - and the candidate from United Russia suddenly received an advantage. Medusa invites readers to solve several interest tasks. Only without miracles!

Lost opportunity

There is a probability of 30%that you will become a governor. You also submitted an application for the first flight around the moon, and there is 0.005%chance that they will choose you. What is the probability that you will be chosen in the space program, but you will not be able to fly, since you will work as a governor?

Answer and solution

0.0015%. You just need to change interest.

(30/100) * (0.005/100) * 100 = 0.0015

A wonderful victory

After counting the votes of the second round in all areas, except for the latter, you lag behind the opponent by four percentage points. To win, you need a miracle: you need to get the support of all 2501 people who have received ballots in the last site. What is the minimum number of voters in such elections? Suppose that there were not a single spoiled ballot in the elections.

Answer and solution

65001.

The minimum number of voting = 2501 people + votes dedicated to the rivals before counting in the last area (take for x).

To equalize the rival, you lack 2500 votes (and you need another voice to win).

The difference of 4% means that you scored 0.48 from X (the total number of votes calculated by that time), and your opponent is 0.52 from X.

0.52*x = 0.48*x + 2500

0.52*x - 0.48*x = 2500

0.04*x = 2500

X = 2500 * 100/4 = 62500

62500 + 2501 = 65001 (desired minimum turnout)

No comments

You have become a governor, but they laugh at you in the media, consider you a crook and a corrupt official. 5 independent publications decided to take you a comment on the strange election results. The press secretary gave them your mobile. About one of them you know that if they take your comment first, they will make a meme from you. You have already missed one call from an unknown number. A new call is heard - what is the probability that this is exactly the very media that you are most afraid of?

Answer and solution

20%. A chance is one of five. The first missed call does not matter.

Text of tasks: Ekaterina Krongauz, Denis Dmitriev. Design: Victor Hodak