Math: probability

Question

1. There are 100 tickets in lottery. One of them has the prize of 50$, three of them - have 25$, fifteen of them - have 5$. What's the probability to win something if I bought two tickets.
2. Participants take cards out of the box. All cards are numbered from 1 to 100. Find the probability that the first taken card isn't number 5.

Answer 1

There are a total of 19 winning tickets. The question is the probability of winning any prize, so the prize levels are not important.

The probability of any single ticket winning (p) is 19/100.The probability of any single ticket losing (q) is 81/100 since p + q = 1

You bought two tickets, and there are four possible outcomes:

Both tickets A and B lose; p = qA x qB = (81/100) x (81/100) = 6561/10000 = 0.6561

Both tickets A and B win; p = pA x pB = (19/100) x (19/100) = 361/10000 = 0.0361

Ticket A wins and ticket B loses; p = pA x qB = (19/100) x (81/100) = 1539/10000 = 0.1539

Ticket A loss and ticket B wins; p = qA x pB = (81/100) x (19/100) = 1539/10000 = 0.1539

The last three outcomes have at least one winning ticket, so add those probabilities to get the overall probability

0.0361 + 0.1539 + 0.1539 = 0.3439

For the second problem. there are 99 cards that are not number 5, so the probability of picking a card that is not 5 is 99/100 = 0.99

Hope this helps