What is the probability that she will get at least eight questions correct? no questions correct? no more than two questions correct?
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.
A student is taking a multiple-choice exam in which each question has two choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place two balls (marked A and B) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are nine multiple-choice questions on the exam. Complete parts (a) through (d) below.
- What is the probability that she will get at least eight questions correct?
- no questions correct?
- no more than two questions correct?
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