Two fair dice are thrown. The probability that difference between the number is (a) two is 2 / 9

step 1 In this problem, let us look at each of the options one by one. For the difference to be two, th

Two fair dice are thrown. The probability that difference...

Key Concepts

Probability and Sample Space

This concept involves understanding that any experiment, such as rolling dice, has a defined set of all possible outcomes called the sample space. When dealing with two dice, the sample space consists of all ordered pairs of numbers that could appear, and knowing its total size is fundamental for calculating probabilities of any event.

Combinatorial Counting

This key concept refers to the systematic method of counting the outcomes that satisfy a particular event in the sample space. It involves enumerating the favorable outcomes and then comparing that count to the total number of outcomes, which is a critical process in solving probability problems.

Absolute Difference

The notion of absolute difference is used to measure the distance between two numbers without considering their order. In problems involving dice, it allows one to focus on the magnitude of the difference between the two dice outcomes, which is essential for determining the probability of events defined by such differences.

Discrete Probability Calculation

This concept underlines the idea that when outcomes are distinct and finite, as with dice, the probability of an event is determined by dividing the number of favorable outcomes by the total number of outcomes in the sample space. This method is central to solving problems in discrete probability.

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