Vents T and Q are independent. Which statement about their probabilities is not necessarily true?
1Choice 1
P(T and Q) = P(T) × P(Q)
2Choice 2
P(T | Q) = P(Q | T)
3Choice 3
P(Q | T) = P(Q)
4Choice 4
P(T | Q) = P(T)

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen