When playing roulette at a casino, a gambler is trying to decide whether to bet $20 on the number 10 or to bet $20 that the outcome is any one of the three possibilities 00 comma 0 comma or 1. The gambler knows that the expected value of the $20 bet for a single number is negative $ 1.05. For the $20 bet that the outcome is 00 comma 0 comma or 1, there is a probability of StartFraction 3 Over 38 EndFraction
of making a net profit of $80 and a StartFraction 35 Over 38 EndFraction
probability of losing $20.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.