Out of 10 lottery tickets, 3 with winnings. Each person can take one ticket. Which event is more likely

Out of 10 lottery tickets, 3 with winnings. Each person can take one ticket. Which event is more likely: the winning ticket will be taken out second or third in line?

Since nothing is said about the first drawn ticket, we will consider the options.

If there are only 10 events, and there are 3 favorable events, then the probability of immediately pulling out a winning ticket according to the Laplace formula is:

P = 3/10;

If the ticket is not drawn, then the second has more chances, since there are already 9 events (tickets) in total, and there are still 3 winning ones:

P = 3/9;

If the ticket is not drawn again, then the third has even more chances, since there are 8 events (tickets) in total, and there are still 3 winning ones:

P = 3/8.

3/8> 3/9, –

Therefore, the probability of taking out a winning ticket first, being in 3rd place in the queue, is higher.

If the first winning ticket was pulled out on the first move, then the probability of getting the third winning ticket out is still higher than that of the second in the queue, since:

If 1 winning ticket is drawn, then there are already 9 events (tickets), and 2 winning ones. So the chances of the second to pull out a ticket are:

P = 2/9;

And the chances of the third:

P = 2/8;

2/8> 2/9.