Given three boxes I, II and III, each containing two coins. In box I, both coins are 1 rupee
coins, in box II, both are 2 rupee coins and in the box III, there is one 1 rupee and one 2 rupee coin.
A person chooses a box at random and takes out a coin. If the coin is of 1 rupee, what is the
probability that the other coin in the box is also of 1 rupee?	Choose the correct choice from the following
A) 1/5	B) 2/3	C) 2/7	D) 3/7	E) 2/5
Let E1, E2 and E3 be the events that boxes I, II and III are chosen, respectively.   Then P(E1) = P(E2) = P(E3) = 1/3   Also, let A be the event that ‘the coin drawn is of 1 rupee'   Then P(A|E1) = P(a 1 rupee coin from bag I) = 2/2= 
<gadget id="calculator">2/2</gadget>
<output>1</output>
1   P(A|E2)= P(a 1 rupee coin from bag II) = 0   P(A|E3) = P(a 1 rupee coin from bag III) = 1/2   the probability that the other coin in the box is of 1 rupee   = the probability that 1 rupee coin is drawn from the box I.   = P(E1|A)   from 2/3ayes' theorem, we know that   P(E1|A) = [P(E1 )P(A|E1 )]/ [P(E1 )P(A|E1 )+P(E2 )P(A|E2 )+P(E3 )P(A|E3 )]   = (1/3 × 1)/(1/3 × 1 + 1/3 × 0 + 1/3 × 1/2)   = (1/3)/(1/3 × 1 + 1/3 × 0 + 1/3 × 1/2)   = (1/3)/(1/3 × 1/6) = (1/3)/(3/6) = (1/3)/2 = 2/3   2/3
<result>B</result>
Given three boxes I, II and III, each containing two coins. In box I, both coins are 1 rupee
coins, in box II, both are 2 rupee coins and in the box III, there is one 1 rupee and one 2 rupee coin.
A person chooses a box at random and takes out a coin. If the coin is of 1 rupee, what is the
probability that the other coin in the box is also of 1 rupee?