Simplify3√2
√6− √3
+
2 √3
√6+ 2
-
4√3
√6− √2

5√3-7√2+2

Step-by-step explanation:

3√2√6−√3+2√3√6+ 2-4√3√6−√2

Bringing the like terms

3√2√6-2√3√6−√2−√3+2

Now we apply the rule which says

√a x√b = √ab

3√(2x6)-2√(3×6)-√2-√3+2

3√(2x2×3)-2√(3×3×2)-√2-√3+2

3×2√3-2×3√2-√2-√3+2

6√3-6√2-√2-√3+2

Bringing the like terms together

6√3-√3-6√2-√2+2

5√3-7√2+2

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