Question

Two friends race against each other in 100-meter and 800-meter races. Of the 200 races they ran this year, the wins, losses, and ties are shown below. 100 meter (Event D) 800 meter (Event E) A won the race (Event A) 30 50 B won the race (Event B) 60 25 A and B tied (Event T) 10 25 B did not win the race today. What length of race was it more likely to have been? 100 meter or 800 meter? How much more likely?

Answer 1

Let makes the table neater. event D= 100m, even E=800m
                                             (Event D) (Event E) 
A won the race (Event A)     30           50
B won the race (Event B)     60           25 
A and B tied (Event T)          10            25

B did not win the race today. What length of the race was it more likely to have been? The question is asking in what event did the chance of B did not win(lose + ties) is more likely. Then, you need to determine the chance for B did not win in both race.
Chance of B did not win 100-m= 30+10/10=40%
Chance of B did not win 800-m= 50+25/10=75%

The difference would be 75%-40%=35% more likely to lose 800-m race