## RonrickDaano 3 years ago There are three caskets of treasure. The first casket contains 3 gold coins, the second casket contains 2 gold coins and 2 bronze coins, and the third casket contains 2 gold coins and 1 silver coin. You choose one casket at random and draw a coin from it. The probability that the coin you drew is gold has the value ab, where a and b are coprime positive integers. What is the value of a+b?

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probability has to be <1. It can't be a product of two integers.

2. kropot72

|dw:1352886878116:dw| $P(gold)=(\frac{1}{3}\times \frac{1}{3})+(\frac{1}{3}\times \frac{1}{3})+(\frac{1}{3}\times \frac{1}{3})+(\frac{1}{3}\times \frac{2}{4})+(\frac{1}{3}\times \frac{2}{3})$

3. kropot72

I drew a probability tree. Such a tree follows a process thru its various stages with probabilities being calculated at each stage. From the starting point, the probability of selecting each one of the three caskets is 1/3. If the first casket is selected then each of the three gold coins has a 1/3 probability of being selected. The selection of a casket and the selection of a coin are separate and independent sub-events. The multiplication theorem of probability states that if a compound event (such as the selection of a particular gold coin from the first basket) is made up of a number of separate and independent sub-events, the probability of the compound event is the product of the separate probabilities of each sub-event. The addition theorem of probability states that if an event (such as selecting a gold coin from any one of the three caskets) can happen in a number of different and mutually exclusive ways, the probability of its happening at all is the sum of the separate probabilities that each event happens.

4. jishan

very good explain........... kro

5. kropot72

@jishan Thanks.