There are three closed boxes one of which contains a prize. If Joe correctly guesses which box has the prize in it he wins the prize. He chooses a box and then one of the remaining two boxes is revealed to be empty. Joe is then given the option to change his mind and choose the other box which is still closed. What is the probability of his winning the prize if he changes his mind?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
There are three closed boxes one of which contains a prize. If Joe correctly guesses
which box has the prize in it he wins the prize. He chooses a box and then one of the
remaining two boxes is revealed to be empty. Joe is then given the option to change his
mind and choose the other box which is still closed. What is the
the prize if he changes his mind?
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