3 coins are put in a bag. 2 of the coins are weighted with the probabi

Serotoninl7

Serotoninl7

Answered question

2021-11-17

3 coins are put in a bag. 2 of the coins are weighted with the probability of flipping heads being two times greater than the probability of flipping tails while the other coin is a fair coin. One of these coins is selected at random and then flipped once. What is the probability that a weighted coin was selected given that heads was flipped?
Conditional probability: Yes or No.

Answer & Explanation

soniarus7x

soniarus7x

Beginner2021-11-18Added 17 answers

Step 1
The probability that a weighted coin was selected given that heads was flipped is obtained below:
Yes, conditional probability.
Baye’s Theorem formula is given below:
P(A1B1)=P(A1)P(B1A1)P(A1P(B1A1)+P(A2)P(B1A2)}
Step 2
Define the events as given below:
A1 - biased coin
A2 - un biased coin
B1 - head was flipped
it is given that, P(A1) is =35=0.6,P(A2) is 0.4(=135),P(B1A1)=34=0.75 and P(B1A2)=12=0.5.
Substitute P(A1) as 0.6, P(A2) as 0.40, P(B1A1) as 0.75 and P(B1A2) as 0.50.
P(A1B1)=P(A1)P(B1A1)P(A1)P(B1A1)+P(A2)P(B1A2)
=(0.6)(0.75)(0.6)(0.75)+(0.40)(0.50)
=0.450.45+0.20
=0.450.65
=0.6923
Thus, the probability that a weighted coin was selected given that heads was flipped is 0.6923.

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