# Probability - high school - math problems

Probability is the measure of the likeliness that an event will occur. The probability (chance) is a value from the interval <0;1> or in percentage (0% to 100%) expressing the occurrence of some event. 0 is impossible event and 1 (100%) means the certainty event.

1. Rectangle In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
2. Ace From complete sets of playing cards (32 cards), we pulled out one card. What is the probability of pulling the ace?
3. Word What is the probability that a random word composed of chars E, Y, G, E, R, O, M, T will be the GEOMETRY?
4. Two doctors Doctor A will determine the correct diagnosis with a probability 93% and doctor B with a probability 79%. Calculate probability of correct diagnosis if patient is diagnosed by both doctors.
5. Dice How many times must throw the dice, the probability of throwing at least one six was greater than 90%?
6. Scrap From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product?
7. Sales From statistics of sales goods, item A buy 51% of people and item B buys 59% of people. What is the probability that from 10 people buy 2 item A and 8 item B?
8. Dices We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
9. Event probability The probability of event P in 8 independent experiments is 0.33. What is the probability that the event P occurs in one experiment (probability is same)?
10. Balls From the urn in which are 7 white balls and 17 red, gradually drag 3-times without replacement. What is the probability that pulls balls are in order: red red red?
11. Events Event P has probability of 0.84. What is the probability that the event P occurs in 3, 5, 7 try.
12. Pizza A school survey found that 12 out of 15 students like pizza. If 6 students are chosen at random, what is the probability that all 6 students like pizza?
13. Hockey players After we cycle five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other?
14. Lottery The lottery is 60000 elk in which 6200 wins. What is the probability that the purchase of 12 elks won nothing?
15. Monty Hall Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. W
16. Family What is the probability that a family with 7 childrens have: exactly 5 girls? 7 girls and 0 boys? Consider the birth probability of a girl is 48.69% and boy 51.31%.
17. Components In the box are 8 white, 4 blue and 2 red components. What is the probability that we pull one white, one blue and one red component without returning?
18. Bulbs The probability that the bulb can operate 4000 hours is 0.3. What is the probability that exactly one of eight bulbs can operate 4000 hours?
19. Raffle How many raffle tickets must be purchased by Peter in raffle with issued 200 tickets if he wants to be sure win at least 3 price? In the raffle draws 30 prices.
20. The dice What is the probability of events that if we throw a dice is rolled less than 6?

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