14) The game show contestant spins a spinner with the letters A through G on it, then either an easy or hard question is picked randomly for her. What is the
probability that the spinner will stop on the letter A and she is given a hard
question?

13

step-by-step explanation:

distance formula is d=√(x2-x1)^2   +   (y2-y1)^2

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation:

32/80  

91/140

the last one 54 doesn't go into 45. 54/100 ?

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