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?

Step-by-step explanation:

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47

step-by-step explanation:

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560