20. A deck for Number Skat consists of the cards in a regular Poker deck, but all Jacks, Queens and Kings are taken out. (a) Consider the random experiment of drawing one card from a well- shuffled deck for Number Skat. What is the size of the sample space? (b) Consider the event E of drawing an Ace, a Two or a Three, all black, from a well-shuffled deck for Number Skat (spades and clubs are black; hearts and diamonds are red). How many outcomes are there in event E? (c) What is the probability of E? (d) What is the probability of not drawing a black card which is an Ace, a Two or a Three? 21. A student is taking a multiple-choice quiz. The quiz has 6 questions, and each question has 4 choices. If the student randomly guesses the answers to each one of the questions, what is the probability that she will get: a) 2 correct answers and 4 wrong answers? b) 3 correct answers and 3 wrong answers? c) 4 correct answers and 2 wrong answers?
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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