If you were flipping a coin, and needed to get 2 heads in a row, what is the probability of getting two heads in a row. Use your probability tree to help. /

1/4

Step-by-step explanation:

If you flip it twice the possible outcomes are

H   H

H   T

T    H

T    T

The chances of you getting H H is 1 / 4.   If you flip it more than twice, the probability changes. Let's try three times. That gives you 8 different choices.

H   H    H     *

H   H    T      *

H   T    H

H   T   T

T   H   H        *

T   H   T    

T   T    H

T   T    T

What this gives is 3 chances out of 8 which is 0.375 and that's better than 0.25

Four would give you an even better result, There are 16 ways of flipping a coin 4 times. The successful results are

H H H H

H H H T

H H T T

H H T H

T H H T

T T H H

H T H H

I'm sure there might be a couple of more, but already you have done better than 3/8

7/16 is almost 1/2

7/16 = 0.4375

I think however that the answer you should submit is 1/4

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.