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Drop a perpendicular from the top left corner down to the base.  You've formed a 30-60-90 triangle so you can use the sine of 30^o to determine that the base of that triangle is 1.  Same on the right hand side.  Add up all the sides and segments of sides and get

sides of trapezoid and top total 2 + 2 + 2

bases of triangles and center segment of trapezoid base total 1 + 2 + 1

So the trapezoid perimeter is 6 + 4 = 10

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How many elements are in the sample space for flipping a coin 8 times?

A. 4 elements

B. 8 elements

C. 16 elements

D. 64 elements

C. P(B∣A) = P(A and B)/P(B)     is false

To see why...let P(A) = 0.2    and let P(B) = 0.4

Then 

P(A and B) / P(B)  =  (0.2)(.0.4) / (0.4)  =  0.2

But P(B IA) should be 0.4 if these are independent because A has no effect on B 

True

If they were independent...then  B would have no effect on A ...so  P( A l B ) = P(A) = 0.4

An argument could be made that since both 2000 and 3 are accurate to only whole numbers, then their quotient should not be carried out to any decimal places either.  so the answer would be 667. 

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B has no effect on A....so  

P( A I B )   = P(A)  =  0.4  is true

The first is symmetric about the origin...so it is odd

The second is also symmetric about the origin...so....odd

The last is symmetric about the y axis....this is characteristic of an even function

2000 / 3   =   666 + 2/3  ≈  666.66667

P(2 girls)  = C(3,2) (1/2)^3  =  3 * (1/8)  =   3/8

You need to consider the order in which they could be born, so the possibilities are:

1st born. 2nd born.  3rd born.

    B.          B.              B

    B.          B.              G

    B.          G.              B

    G.          B.              B

    B.          G.              G

    G.          B.              G

    G.          G.              B

    G.          G.              G

So the probability of exactly 2 girls and 1 boy is 3/8.

deleted.... see below

D. P(A) * P(B) = P(A and B)

a₁  = 2

a_n  = (1/3)a_{n - 1}

The explicit rule is

a_n  = 2(1/3)^n-1

B is correct

No, there isn't

When a coin is tossed twice the sample space, there are 2^2 elements. when a coin is tossed three times the sample space contains 2^3 elements and so on. So, when a coin is tossed eight times the sample space contains 2^8 = 256 elements

-could it be there is another option over the page?

If independent   P(A and B )  = P(A) * P(B)...so.....

(0.5) (0.2)  =  0.1

D. P(A) = 0.5, P(B) = 0.2, P(A and B) = 0.1

If independent 

P ( A and B)  =  P(A) * P(B)  = (0.5) (0.3)  = 0.15

ES.....I'm guessing that you want P( 1 red and 2 yellow)   (???)

If so...we have

We have

C(5, 1) * C(5, 2)              5  * 10                50                5

______________  =     _________  =    _____   =     ___

    C(10, 3)                         120                 120              12

Any of these is right with justified meaning.

e.g. if you picked A

By using the word "instinct", Orwell reinforces the idea that writing is a natural process that all people have an innate desire to participate in. This connotates that...(etc).

1/2  of the natural numbers from 1 to 50  are even

So

P(even)  = 1/2   =  equally likely

the first statement fits best from the info given

P(1 three)  =  C(10, 1) (1/6) (5/6)^9  ≈  .323  ≈   32.3%