A box contains 3 coins. One coin has 2 heads and the other two are fair. A coin is chosen at random from the box and flipped. If the coin turns up heads, what is the probability that it is the two-headed coin? Is the answer 1/3? Was the answer intuitive?

Respuesta :

Answer: Our required probability is [tex]\dfrac{1}{2}[/tex]

Step-by-step explanation:

Since we have given that

Number of coins = 3

Number of coin has 2 heads = 1

Number of fair coins = 2

Probability of getting one of the coin among 3 = [tex]\dfrac{1}{3}[/tex]

So, Probability of getting head from fair coin = [tex]\dfrac{1}{2}[/tex]

Probability of getting head from baised coin = 1

Using "Bayes theorem" we will find the probability that it is the two headed coin is given by

[tex]\dfrac{\dfrac{1}{3}\times 1}{\dfrac{1}{3}\times \dfrac{1}{2}+\dfrac{1}{3}\times \dfrac{1}{2}+\dfrac{1}{3}\times 1}\\\\=\dfrac{\dfrac{1}{3}}{\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{3}}\\\\=\dfrac{\dfrac{1}{3}}{\dfrac{2}{3}}\\\\=\dfrac{1}{2}[/tex]

Hence, our required probability is [tex]\dfrac{1}{2}[/tex]

No, the answer is not [tex]\dfrac{1}{3}[/tex]

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