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.

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?

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.

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?

myrraarrym · Answer

this is the table

luffingsails · Answer

So, which race is A more likely to have won given the outcomes? Can you calculate that?

myrraarrym · Answer

A is more likely to win 800 meters and B is more likely to win the 100 meter?

luffingsails · Answer

Right, so if A is more likely to win the 800m race and A won today. What was the likely race?

The 800m right?

myrraarrym · Answer

yes. but how much more likely is B to lose 800 meters?

luffingsails · Answer

So, calculate the probability of B losing the race for each race. The difference between the two is the "much more likely" answer.