# Probability + binomial distribution - 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: 26

• 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.
• 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
• 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
• Family
94 boys are born per 100 girls. Determine the probability that there are two boys in a randomly selected family with three children.
• Boys and girls
There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them?
• Internet anywhere
In school, 60% of pupils have access to the internet at home. A group of 8 students is chosen at random. Find the probability that a) exactly 5 have access to the internet. b) At least 6 students have access to the internet
• Families 2
There are 729 families having 6 children each. The probability of a girl is 1/3 and the probability of a boy is 2/3. Find the the number of families having 2 girls and 4 boys.
• Left handed
It is known that 25% of the population is left-handed. What is the probability that there is a maximum of three left-handers at a seminar where there are 30 participants?
• Component fail
There is a 90 percent chance that a particular type of component will perform adequately under high temperature conditions. If the device involved has four such components, determine the probability that the device is inoperable because exactly one of the
• Dice
We throw 10 times a play dice, what is the probability that the six will fall exactly 4 times?
• Dice
We throw five times the dice. What is the probability that six fits exactly twice?
• Test
The teacher prepared a test with ten questions. The student has the option to choose one correct answer from the four (A, B, C, D). The student did not get a written exam at all. What is the probability that: a) He answers half correctly. b) He answers al
• Distribution function
X 2 3 4 P 0.35 0.35 0.3 The data in this table do I calculate the distribution function F(x) and then probability p(2.5
• 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?

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...