Ron randomly pulls a pen out of a box that contains 1 red, 2 black, and 3 blue pens. He does this 4 times, replacing the pen each time, but pulls out a blue pen only 1 time. Ron concludes
that the observed frequency of pulling a blue pen will eventually be closer to the expected
frequency based on the theoretical probability of pulling a blue pen. Which reasoning best
supports his conclusion?

range is infinite on both x and y axis positive and negative

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

the real question is why is this guys last name heavyfoot

step-by-step explanation:

step-by-step explanation: