A process for making plate glass produces small bubbles (imperfections) scattered at random in the glass, at an average rate of four small bubbles per 10m2. Consider glass pieces with 4. dimensions 2.5m x 2.0m. (i) Quantify the probability that a piece of glass contains at least one small bubble. (ii) Calculate the probability that five glass pieces chosen at random are all free of bubbles. (iii) Suppose ten glass pieces were randomly chosen. Write the probability that 5 of the pieces contain at least one small bubble each?
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.
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