Percentages + combinatorial number - math problems

Number of problems found: 16

• travel agency
Small travel agency offers 5 different tours at honeymoon. What is the probability that the bride and groom choose the same tour (they choose independently)?
• Family
94 boys are born per 100 girls. Determine the probability that there are two boys in a randomly selected family with three children.
• Three reds
What is the probability that when choosing 3 carats from seven carats, all 3 reds will be red?
• Two aces
From a 32 card box we randomly pick 1 card and then 2 more cards. What is the probability that last two drawn cards are aces?
• 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?
• 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
• 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.
• 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%.
• Hazard game
In the Sportka hazard game, 6 numbers out of 49 are drawn. What is the probability that we will win: a) second prize (we guess 5 numbers correctly) b) the third prize (we guess 4 numbers correctly)?
• 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
• Covid-19
Data showed that 22% of people in a small town was infected with the COVID-19 virus. A random sample of six residents from this town was selected. Find the probability that exactly two of these residents was infected.
• 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?
• Sick days
In Canada, there are typically 261 working days per year. If there is a 4.9% chance that an employee takes a sick day. .. what is the probability an employee will use 17 OR MORE sick days in a year?
• Wimbledon finals
Serena Williams made a successful first serve 67% 0f the time in a Wimbledon finals match against her sister Venus, If she continues to serve at the same rate the next time they play and serves 6 times in the first game, determine the probability that: 1.
• Sum on dice
We have two dice. What is the greater likelihood of fall a total sum 7 or 8 ? (write 7, 8 or 0 if the probabilities are the same)?
• STRESSED word
Each letter in STRESSED is printed on identical cards, one letter per card, and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled.

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...