An experiment consists of tossing a die and then flipping a coin once if the number on the die is even. If the number on the die is odd, the coin is flipped twice. Using the notation 4HH, for example, to denote the outcome that the die comes up 4 and then the coin comes up heads, and 3HTHT to denote the outcome that the die comes up 3 followed by a head and then a tail on the coin, construct a tree diagram to show the 18 elements of the sample space SS. For the sample space SS
(a) list the elements corresponding to the event AA that a number less than 3 occurs on the die;
(b) list the elements corresponding to the event BB that two tails occur;
(c) list the elements corresponding to the event A′A ′;
(d) list the elements corresponding to the event A′∩BA ′ ∩B;
(e) list the elements corresponding to the event A∪BA∪B.

Kindly check attached picture for sample space.

Step-by-step explanation:

Sample space, S

S = {1HH, 1HT, 1TT, 1TH, 2H, 2T, 3HH, 3HT, 3TT, 3TH, 4H, 4T, 5HH, 5HT, 5TH, 5TT, 6H, 6T}

The tree diagram for all 18 elements in the sample space can be found in the picture attached below :

a.)

Event A ; number on die < 3

A = {1HH, 1HT, 1TT, 1TH, 2H, 2T}

b.)

Event B ; 2 tails occur :

B = {1TT, 3TT, 5TT}

QUESTIONS B, C and E are not well formatted

for the points

step-by-step explanation:

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3