Given three identical boxes I, II and III each containing two coi… - Vidyadip

Question

Given three identical boxes I, II and III each containing two coins. In box I, both coins are gold coins, in box II, both are silver coins and in box III, there is one gold and one silver coin. A person chooses a box at random and takes out a coin. If the coin is of gold, what is the probability that the other coin in the box is also of gold?

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Answer

Let E₁: selecting box I, E₂: selecting box II and E₃: selecting box III

$\therefore$ P (E₁) = P (E₂) = P (E₃) = $\frac{1}{3}$

let event A: Getting a gold coin

$\therefore$ P (A/E₁) = 1 P (A/E₂) = 0 P (A/E₃) = $\frac{1}{2}$

P(E₁/A) = $\frac{\text{P(E}_{1})\cdot\text{P(A/E}_{1})}{\text{P(E}_{1})\text{P(A/E}_{1})+\text{P(E}_{2})\text{P(A/E}_{2})+\text{P(E}_{3})\text{P(A/E}_{3})}$

= $ \frac{\frac{1}{3}\cdot1}{\frac{1}{3}\cdot1+0+\frac{1}{3}\cdot\frac{1}{2}}=\frac{2}{3}$.

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