Take a Penny, Leave a Penny - Chapter 4 and 5 - Rand2 1
From 24/SP-STA-2023-88010 Elem Stats
Suspicious or Not?
An airline has just finished training 25 junior pilots (15 male and 10 female) to become captains. Unfortunately, only 8 captain
positions are available right now. Airline management announces that a lottery process to determine which junior pilots would be
selected to fill the available captain positions. The airline management wrote the names of all 25 junior pilots on identically sized
slips of paper, placed all of the slips of paper in a hat, mixed the slips of paper in the hat thoroughly, and then randomly selected a
total of 8 slips of paper (one slip at a time) from the hat. Those 8 slips of paper were the junior pilots who were given the
available captain positions.
The results: of the 8 junior pilot names selected, 5 were female and 3 were male.
To Investigate & Discuss
Some of the male pilots who were not selected are suspicious about the results. Mathematically, are their suspicions reasonable?
How likely is it for this lottery to end up with exactly 5 females and 3 males?