By the interior angles theorem, if angle a is 25 degrees and angle b is greater than 51 degrees but less than 57 degrees what are the possible measurements for angle c

I guess you are talking about a triangle . The 3 angles add up to 180 degrees.

b +  c = 180 - 25 = 155 degrees

When   b  > 51 degrees  then

c  <= 155 - 52

c <= 103 degrees

When b < 57

c >= 155 - 56

c >= 99 degrees

Possible measurements  for angle c :=

99   =<  c  <= 103  (answer).

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