Find the exact numbers to answer each of the following questions. You do not need to show any justification for this, but you will only earn the bonus points if at least 4 out of 5 of your answers are correct. i. How many 5-letter passwords(letter may be repeated) can be created from the monkey type writer from Ql if it is forbidden for a password to begin and end with the same k tter? Answer: ii. Using the monkey typewriter from Q1, how many 8-letter words are there consisting of 8 distinct letters that contain the word APE' (as 3 consecutive )letters within the 8-letter word? Answer: iii. In a strange experiment involving N monkeys, we let each monkey create one 2 -letter password with the monkey typewriter( letters may be repeated). What is the exact minimum number N of monkeys needed in order to guarantee that we will see the same 2 letter password created by at least 5 of the N monkeys? (each monkey is free to choose whatever random password it wishes, regardless of whatever passwords the other monkeys have chosen).
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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