A regular dodecagon P_1 P_2 P_3 \dotsb P_{12} is inscribed in a circle with radius 1. Compute (P_1 P_2)^2 + (P_1 P_3)^2 + \dots + (P_{11} P_{12})^2.(The sum includes all terms of the form (P_i P_j)^2, where 1 \le i < j \le 12.)

Hint(s): Sums of squares of lengths should make you think of what?

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

it would be 3 ÷by 6 because the number on each side

a natural event such as a flood, earthquake, or hurricane that causes great damage or loss of life.

step-by-step explanation: