Suppose that we have a box that contains two coins: A fair coin: P(H)=P(T)=0.5 . A two-headed coin: P(H)=1 . A coin is chosen at random from the box, i. e. either coin is chosen with probability 1/2 , and tossed twice. Conditioned on the identity of the coin, the two tosses are independent. Define the following events: Event A : first coin toss is H . Event B : second coin toss is H . Event C : two coin tosses result in HH . Event D : the fair coin is chosen. For the following statements, decide whether they are true or false. A and B are independent.

2 . True

Step-by-step explanation:

2. The two events are mutually exclusive events. This means that the probabilities on coins 1 and coins 2 are independent on each other. In other words, the probability of the first coin does not affect the probability of the second coin outcome.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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