An astronaut spends 53% of the day working, 0.1 of the day eating, 3/10 of the day sleeping, and the rest of the day exercising. Order the events by duration from least to greatest.

0.1 of the day eating; 3/10 of the day sleeping; 53% of the day working

Step-by-step explanation:

convert all to decimals

0.1=0.1

3/10=0.3

53%=0.53

least to greatest= 0.1, 0.3, 0.53

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