Cindy says she found a shortcut for doing multiplication problems. When she multiplies 3x24, she says,"3x4 is 12ones, or 1ten and 2ones. Then, there’s just 2tens left In 24, so add it up, and you get 3tens and 2ones." Do you think Cindys shortcut works? Explain your thinking in words, and justify your response using a model or partial products.

5050 i think

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