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Suppose you flip three fair, mutually independent coins. Define the following events: Let A be the event that the first coin is heads. Let B be the event that the second coin is heads. Let C be the event that the third coin is heads. Let D be the event that an even number of coins are heads. Determine the probability space for this experiment (build the probability tree). Using the probability tree, find the probability of each of the events A, B, C, D, (A AND C), (A AND B AND C), (A OR B OR C

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yemmy

Answer:

P(A)=1/2

P(B)=1/2

P(C)=1/2

P(D)=5/8

P(AandC)=1/4

P(AandBandC)=1/8

P(AorBorC)=7/8

Step-by-step explanation:

The total number of possible outcome or the sample space for this Question is given as follows

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

n(S) = 8

A = {HHH, HHT, HTH, HTT}

n(A) = 4

B = {HHH, HHT, THH, THT}

n(B) = 4

C = {HHH, HTH, THH, TTH}

n(C) = 4

D = {HHH, HHT, HTH, THH, TTT}

n(D) = 5

check the attached files for the Probability tree

as well as additional solution to the qustion

Ver imagen yemmy
Ver imagen yemmy
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Answer:

Please read the answers below.

Correct statement and question:

Suppose you flip three fair, mutually independent coins. Define the following events:  

  • Let A be the event that the first coin is heads.
  • Let B be the event that the second coin is heads.
  • Let C be the event that the third coin is heads.
  • Let D be the event that an even number of coins are heads.

1. Determine the probability space for this experiment (build the probability tree).

2. Using the probability tree, find the probability of each of the events A, B, C, D, (A AND C), (A AND B AND C), (A OR B OR C).

Source:

Previous question that can be found at brainly

Step-by-step explanation:

1. Let's determine the probability space, building the probability tree, this way:

Flip                    1           2         3          4         5       6            7        8

First Coin       Heads Heads Heads Heads Tails Tails     Tails   Tails

Second Coin Heads Heads Tails     Tails     Tails Heads Tails   Heads

Third Coin     Heads Tails     Tails     Heads  Tails Tails    Heads Heads

Events            A, B, C  A, B, D   A       A, C, D     -      B          C       B, C, D

2. Let's find all the probabilities of the events requested using the results from question 1, this way:

P (A) = 4/8 = 1/2

P (B) = 4/8 = 1/2

P (C) = 4/8 = 1/2

P (D) = 3/8

P ( A and C) = 2/8 = 1/4

P (A AND B AND C) = 1/8

P (A OR B OR C) = 7/8

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