. A coin is tossed three times, and the sequence of heads and tails is recorded.(a) Determine the sample space, Ω.(b) List the elements that make up the following events: i. A= exactly two tails, ii. B= at least twotails, iii. C= the last two tosses are heads(c) List the elements of the following events: i. A, ii. A∪B, iii. A∩B, iv. A∩C

See explanation below

Step-by-step explanation:

Here a coin was tossed three times.

Let H = head &  T = tail

Find the following:

a) The sample space:

Since a coin is tossed thrice, all possible outcome would be:

S = { HHH, HHT, HTH, HTT, TTT, TTH, THH, THT}

b) i) A = Exactly 2 tails: Here exactly 2 tails were recorded.

A = {HTT, TTH, THT}

ii) B = at least two tails: Here 2 or more tails were recorded.

B = {HTT, TTT, TTH, THT}

iii) C = the last two tosses are heads:

C = { HHH, THH}

c) List the elements of the following events:

i) A. This means all outcomes in A

= {HTT, TTH, THT}

ii) A∪B. A union B, means all possible outcomes present in A or B or in both

= {HTT, TTH, THT, TTT}

iii) A∩B. This means all possible outcomes of A that are present in B.

= {HTT, TTH, THT}

iv) A∩C. All outcomes A that are present in B

= {∅}

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation:

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus