Problem of the Week - Algebra and Up - May 2, 2021 to May 8, 2021

Algebra and Up: 

Question: There are 100 marbles in a bag. They've numbered 0, 1, 2, all the way through 99. What is the probability that if you draw three marbles out of the bag at random without replacing them, the number on the first marble will be 0, the number on the second will be 1, and the number on the third will be 2? 

Answer: 1 out of 970,200

Solution: The probability of drawing the 0 first is 1/100. If the marble isn't replaced, then the probability of drawing the 1 next is 1/99. Then, the probability of drawing the 2 next is 1/98. So, the probability of drawing exactly those numbers in that order is 1/100x99x98 = 1/970200