A fair coin is tossed three times and the events A, B, and C are defined as follows: A: \{ At least one head is observed \} B: \{ At least two heads are observed \} C: \{ The number of heads observed is odd \} Find the following probabilities by summing the probabilities of the appropriate sample points (note that 0 is an even number):

(a) P(A) =
(b) P(A \textrm{ or } B) =
(c) P((\textrm{not }A) \textrm{ or } B \textrm{ or } (\textrm{not }C)) =

a)

b)

c)

Step-by-step explanation:

Given : A fair coin is tossed three times and the events A, B, and C are defined as follows: A: At least one head is observed, B: At least two heads are observed, C: The number of heads observed is odd.

To find : The following probabilities by summing the probabilities of the appropriate sample points ?

Solution :

The sample space is

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

n(S)=8

A: At least one head is observed

i.e. A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}

n(A)=7

B: At least two heads are observed

i.e. B={HHH,HTT,TTH,THT}

n(B)=4

C: The number of heads observed is odd.

i.e. C={HHH,HTT,THT,TTH}

n(c)=4

a) Probability of A, P(A)

b) P(A or B)

Using formula,

(c) P((not A)  or B  or (not C))

A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}

not A = {TTT} = 1

B={HHH,HTT,TTH,THT}

C={HHH,HTT,THT,TTH}

not C = {HHT,HTH,THH,TTT} = 4

So, not A or B or not C = {HHH,HHT,HTH,THH,TTT}=5

21

step-by-step explanation:

the answer is thin because within context, the stanza concludes the and frail tone the people have toward each other, and the fact that it would be thin, makes the most sense compared to "pliable" or "not hard or firm to the touch". hope this , good luck.

step-by-step explanation:

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