SOLUTION: A box A contains 4 gold rings and 3 diamond rings. A box B contains 2 gold rings and 5 diamond rings. A ring is picked at random from box A and placed in box B. A ring is then pick

Question 1199439: A box A contains 4 gold rings and 3 diamond rings. A box B contains 2 gold rings and 5 diamond rings. A ring is picked at random from box A and placed in box B. A ring is then picked at random from box B and placed in box A. Determine the probability that:(a).box A has the same number of gold and diamond rings as it did initially. (b).box A has more gold rings than it did initially.
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
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A box A contains 4 gold rings and 3 diamond rings.
A box B contains 2 gold rings and 5 diamond rings.
A ring is picked at random from box A and placed in box B.
A ring is then picked at random from box B and placed in box A.
Determine the probability that:
(a) box A has the same number of gold and diamond rings as it did initially.
(b) box A has more gold rings than it did initially.
~~~~~~~~~~~~~~~~

(a)  Case (a) may happen if and only if any one of these two two-step events will happen

          (1) EITHER a gold    ring is picked from A to B and a gold    ring is then picked from B to A,

          (2)   OR   a diamond ring is picked from A to B and a diamond ring is then picked from B to A.


         The probability of the two-step event (1) is P =  = .

         The probability of the two-step event (2) is P =  = .


         Thus the probability of case (a) is  P(a) =  =  = .   ANSWER



(b)  Case (b) may happen if and only if any this one two-step event will happen

          a diamond ring is picked from A to B and a gold ring is then picked from B to A.


         The probability of this two-step event is P(b) =  = .    ANSWER.

Solved and fully explained.

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