Combinatorics + time - practice problems
Number of problems found: 49
- Five roommates
Five roommates will move into a house with four bedrooms: one double room and three single rooms. The five roommates propose that they draw names to determine the order in which they pick the bedrooms, assuming that the first three names drawn will choose - Richard
Richard is conducting an experiment. Every time he flips a fair two-sided coin, he also rolls a six-sided die. What is the probability that the coin will land on tails and the die will land on an even number? - A basket 4
A basket contains 9 fruits, where 4 are oranges, and the rest are mangoes. Three fruits are taken out one at a time and put aside. Find the probability that 3 are oranges. - False positive, false negative
Suppose the likelihood of someone being allergic to cats is 1/1000 of the general population. A test to determine if you're allergic to cats has a false positive rate of 5%; that is, 5% of the time, the test will indicate incorrectly that you are allergic
- Bulb life
Tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. Find the probability that a randomly selected light bulb will last between 675 and 900 hours. - Ekene and Amina
The probability that Ekene will be alive in 5 years' time is 3/4, and the probability that his wife Amina will be alive in 5 years' time is 2/5. Find the probability that in 5 years' time: a) both of them will be alive b) only Ekene will be alive - Possibilities 36911
There are seven fountains in the city. Only five always work. How many possibilities do five fountains work at the same time? - Probability 34801
Last year, it rained 12 days in March. What is the probability that it rained on March 20? - Chords
How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
- Volleyball
Eight girls want to play volleyball against boys. On the field at one time can be six players per team. How many initial teams of these girls may be trainers to choose from? - Three digits number 2
Find the number of all three-digit positive integers that can be put together from digits 1,2,3,4 and which are subject to the same time has the following conditions: on one position is one of the numbers 1,3,4, on the place of hundreds 4 or 2. - Altogether 69994
Twelve players signed up for the squash tournament. Based on the lottery, they formed pairs, and in the first round, each pair played one match. The winners advanced to the second round, where they played each other one game at a time. How many matches we - Goalkeeper
Mike plays as the goalkeeper 50% of the time if Peter is the coach in a football game. But if Robert is coaching, he only has a 30% chance. Peter coaches more than Robert in about 6 to 10 games. What is the probability that Mike gets to be the goalie toda - Ten dices
When you hit ten dice simultaneously, you get an average of 35. How much do you hit if every time you get six, you're throwing the dice again?
- Participated 81728
The school volleyball tournament was played on a one-on-one basis. One match lasted 15 minutes, and 3 hours and 45 minutes were played. Calculate how many teams participated. - Differently 22543
Jasmine is a big paradise. She wants to go differently dressed every day. She has four different shoes, seven skirts, 8 T-shirts, and three hair ornaments. How many days can an outfit be combined each time? - Probability 63434
There are tickets with the numbers 1, 2, 3, 4, 5, 6, 7, and 8 in the envelope. Two tickets are drawn from the envelope at a time. What is the probability that the sum of the numbers drawn will be 7? Write the result as a decimal rounded to hundredths. - The big clock
The big clock hands stopped at a random moment. What is the probability that: a) a small hand showed the time between 1:00 and 3:00. b) the big hand was in the same area as a small hand in the role of a)? c) did the hours just show the time between 21:00 - Permutations with repetitions
How many times can the input of 1.2.2.3.3.3.4 be permutated into four digits, three digits, and two digits without repetition? Ex: 4 digits = 1223, 2213, 3122, 2313, 4321. . etc 3 digits = 122.212.213.432. . etc 2 digits = 12, 21, 31, 23 I have tried the
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