One way of proving that two REs are equivalent is to construct their minimized DFAs and then compare them. If they differ only by state names, then the REs are equivalent. Use this technique to check the following pairs of REs and state whether or not they are equivalent. (a) (0 | 1)* and (0* | 10*)* (b) (ba) (a*b* | a*) and (ba)*ba (b*|)

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

0.50 , 0.75

step-by-step explanation: