In a Go match between the Amy team and Ben team, a game is played on each of board \( 1 \), board \( 2 \), board \( 3 \) and board \( 4 \). On each board, the probability that the Amy team wins is \( 0.2 \), the probability of a draw is […]

# Counting Techniques

# Factorial Notation

$n!$ is the product of the first $n$ positive integers for $n\ge 1$. $$n!=n(n-1)(n-2)(n-3) \cdots \times 3 \times 2 \times 1$$ $n!$ is read "$n$ factorial". For example, the product $5 \times 4 \times 3 \times 2 \times 1$ can be written as $5!$. Notice that $5 \times 4 \times 3$ can be written using [...]

# Probability with Replacement

Probability with Replacement is used for questions where the outcomes are returned back to the sample space again. Which means that once the item is selected, then it is replaced back to the sample space, so the number of elements of the sample space remains unchanged. A jar contains five balls numbered 1, 2, 3, [...]

# Probability Ratio using Combination

Counting Techniques for Probability Ratio using Combination The probability ratio of an event is the likelihood of the chance that the event will occur as a result of a random experiment, and it can be found using the combination. When the number of possible outcomes of a random experiment is infinite, the enumeration or counting [...]