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
Algebra ->
Finance
-> 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
Log On
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(52781) (Show Source):
You can put this solution on YOUR website! .
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.
