Summary: Problems Of The Week
Due March 5th
Make sure to review the guidelines before you start!
You can also look at Solutions to Past Problems on the website!
Please Write Solutions Clearly and Neatly.
1. Consider the square having as vertices the following points (-1,1), (1,1), (1,-1), and (-1,-1) .
Find the probabilty that a randomly selected point inside the square will have the sum of its
coordinates greater than 1/3 . Write your answer as a common fraction in lowest term.
2. We have 4 girls and 2 boys to be seated in a 6-seat row at the movie theater. What is the
probability that the two people at each end of the row were both boys or both girls? Express your
answer as a common fraction in lowest term.
3. Daniel chooses a diagonal from a regular polygon having 8 sides . Celine chooses another
diagonal from the same polygon. What is the probability that they chose two diagonals of the
same length? Give your answer as a common fraction in lowest terms.
4. We randomly select 4 prime numbers without replacement from the first 16 prime numbers.
What is the probability that the sum of the four selected numbers is odd? Express your answer as
a common fraction in lowest terms.
5. A student ID number at a certain university consists of a 6-digit number, such as 023452 .
What is the probability that a randomly selected student ID be such that no two of its digits are
the same? Express your answer as a decimal to the nearest thousandths.