We have a bag of three biased coins a, b, and c with probabilities of coming up heads of 20%, 60%, and 80%, respectively. One coin is drawn randomly from the bag (with equal likelihood of drawing each of the three coins), and then the coin is flipped three times to generate the outcomes x1, x2, and x3. I.) draw the bayesian network corresponding to this setup and define the necessary cpts. Ii.) calculate which coin was most likely to have been drawn from the bag if the observed flips come out heads twice and tails once. Justify your answer.
Answers
Answer:
(i) 3 coins⇒ 1 coin chosen⇒Probability of H/T(3times)⇒Likely coin.
(ii) A
Step-by-step explanation:
Concept= Bayes Theorem of probability
Given= Probability of 3 coins and outcome of 3 flips
To find= Probability of chosen coin out of 3 given
Explanation=
We have been given three coins A, B and C and their probability of Heads.
A : Heads 20% =0.2 , Tails 80% =0.8
B : Heads 60% = 0.6 , Tails 40% = 0.4
C : Heads 80% = 0.8 , Tails 20% = 0.2
If one coin is chosen at random probability will be 1/3 =0.33
(i) Bayesian Network is
3 coins⇒ 1 coin chosen⇒Probability of H/T(3times)⇒Likely coin..
(ii) Probability
If there are three outcomes as x1, x2, and x3. We have to restrict ourself to two head and one tail
Probability of A heads, B heads and C tails = 0.33/(0.2+0.6+0.2)=0.33
Probability of A heads, C heads and B tails = 0.33/(0.2+0.4+0.8)= 0.26
Probability of C heads, B heads and A tails = 0.33/(0.8+0.60+0.8)= 0.15
Observing this probability Definitely it will be the coin A or C
Probability of outcomes/Probability of Choosing coin=
A= 0.33/0.33=1
C=0.26/0.33=0.79
So clearly it is A.
#SPJ1
Answer:
Step-by-step explanation:
Here we will use " Bayes Theorem of probability"
Given= Probability of 3 coins and outcome of 3 flips
To find= Probability of chosen coin out of 3 given
We have given three coins A, B and C and their probability of Heads.
A : Heads 20% =0.2 , Tails 80% =0.8
B : Heads 60% = 0.6 , Tails 40% = 0.4
C : Heads 80% = 0.8 , Tails 20% = 0.2
If one coin is chosen at random probability will be 1/3 =0.33
(i) Bayesian Network is
3 coins⇒
1 coin chosen= Probability of H/T(3times)= Likely coin..
(ii) Probability
If there are three outcomes as x1, x2, and x3. We have to restrict ourself to two head and one tail
Probability of A heads, B heads and C tails = 0.33/(0.2+0.6+0.2)=0.33
Probability of A heads, C heads and B tails = 0.33/(0.2+0.4+0.8)= 0.26
Probability of C heads, B heads and A tails = 0.33/(0.8+0.60+0.8)= 0.15
By observing all this we can say that A and C probability can be taken.
Probability of outcomes/Probability of Choosing coin=
A= 0.33/0.33=1
C=0.26/0.33=0.79
So we can say 0.33/0,33
=1
Hence A is correct.