Amanda's penny bank is 2/3 full.
after she removes 100 pennies, it is 4/9 full
full how many pennie
can amanda's bank hold?
pennies

450 pennies

Step-by-step explanation:

2/3 ➡ 3/3 × 2/3 = 6/9

let's call it 9x

the bank contains 6x after she removes 100 pennies 4x is left

which means 2x = 100 pennies and x = 50 pennies

therefore the bank can carry 50 × 9 = 450 pennies

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