# what are the odds

Suppose that each event in a consecutive sequence of events has 5 equally likely outcomes. The probability of a particular outcome among the possible outcomes of an individual event is 0.20. In a sequence of 20 consecutive events, how many different sequences of outcomes are possible? Write it using Excel’s notation for a power (3^2 = 9, 10^3 = 1000).

Odds expresses the ratio of how often an event of interest occurs to how often it does not occur. For example, if the probability of failure is 25%, the odds of failure are 1 failure to 3 successes, or 1:3. If failure occurs 1 time to successes 3 times, the probability of failure is 1/(1+3). Let’s apply this to 2 sequences of 20 consecutive events running simultaneously.

What is the probability that the first event in both sequences have the same outcome? What are the odds of having the same outcome?

What is the probability of the first and second event matching in both sequences? What are the odds of having the same outcome in both the first and second event?