# 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.

#### Number of problems found: 114

• Three colors Find the probability that 3 balls of the same color will be drawn from fate with 10 white, 10 red, and 10 blue balls.
• Playing cards From 32 playing cards containing 8 red cards, we choose 4 cards. What is the probability that just 2 will be red?
• Six questions test There are six questions in the test. There are 3 answers to each - only one is correct. In order for a student to take the exam, at least four questions must be answered correctly. Alan didn't learn at all, so he circled the answers only by guessing. What
• Probability of failures In certain productions, the probability of failures is 0.01. Calculate the probability that there will be more than 1 failure among the 100 selected products if we return the selected products to the file after the check. How large must the group of people be so that the probability that two people have a birthday on the same day of the year is greater than 90%?
• All use computer It is reported that 72% of working women use computers at work. Choose 3 women at random, find the probability that all 3 women use a computer in their jobs.
• The test The test contains four questions, and there are five different answers to each of them, of which only one is correct, the others are incorrect. What is the probability that a student who does not know the answer to any question will guess the right answer
• Double probability The probability of success of the planned action is 60%. What is the probability that success will be achieved at least once if this action is repeated twice?
• Alarm systems What is the probability that at least one alarm system will signal the theft of a motor vehicle when the efficiency of the first system is 90% and of the independent second system 80%?
• Table and chairs Four people should sit at a table in front of a row of 7 chairs. What is the probability that there will be no empty chair between them if people choose their place completely at random?
• Fall sum or same Find the probability that if you roll two dice, it will fall the sum of 10, or the same number will fall on both dice.
• Birth Let's assume that the probability of the birth of a boy and a girl in the family is the same. What is the probability that in a family with five children, the youngest and oldest child is a boy?
• Pairs of socks Ferdinand has twelve pairs of socks, one sock is leaky. What is the probability of putting on a leaky sock?
• Ball bearings One bearing is selected from the shipment of ball bearings. It is known from previous deliveries that the inner bearing radius can be considered as a normal distribution of N (µ = 0.400, σ2 = 25.10^−6). Calculate the probability that the selected radius w
• Records Records indicate 90% error-free. If 8 records are randomly selected, what is the probability that at least 2 records have no errors?
• Genetic disease One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting the disease. A family has 3 children. What is the probability of this family having one child who inherited
• Probability of malaria A survey carried out at a certain hospital indicates that the probability that a patient tested positive for malaria is 0.6. What is the probability that two patients selected at random (i) one is negative while the other tested positive? (i) both patient
• Today in school There are 9 girls and 11 boys in the class today. What is the probability that Suzan will go to the board today?
• One three We throw two dice. What is the probability that max one three falls?
• Lathe 95% of the components manufactured on the lathe comply with the standard, of which 80% of the components are first-class. How likely can we expect a manufactured part to be first class?

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