We can rewrite the expression under the radical as
then taking the fourth root, we get
Why the absolute value? It's for the same reason that
since both and
return the same number
, and
captures both possibilities. From here, we have
The absolute values disappear on all but the term because all of
,
and
are positive, while
could potentially be negative. So we end up with
Answer:
24/35, about 69%
Step-by-step explanation:
The data given can be put into a 2-way table (attached). It shows that 0.48 of all calls were answered and resulted in a mortgage application. Altogether, 0.70 of all calls resulted in a mortgage application. Thus the conditional probability of interest is ...
p(spoke to attendant | applied for a mortgage) = p(spoke & applied)/p(applied)
= 0.48/0.70 = 24/35 ≈ 69%
