There are one coin and a pair of dice. Suppose we flip the coin and roll the pair of dice at the same time. For the coin, if it turns out to be heads, we will get two points. On top of that, we will get points equal to the sum of two numbers from each dice. Let's define a sample space, S, as all possible pointsd we can get. What is P({Get a point equal to either 7 or 8 or 9})? What is P({Get a point equal to either 7 or 8 or 9} | {Get the tail coin})?
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.
There are one coin and a pair of dice. Suppose we flip the coin and roll the pair of dice at the same time. For the coin, if it turns out to be heads, we will get two points. On top of that, we will get points equal to the sum of two numbers from each dice. Let's define a
What is P({Get a point equal to either 7 or 8 or 9})?
What is P({Get a point equal to either 7 or 8 or 9} | {Get the tail coin})?
There are one coin and a pair of dice. Suppose we flip the coin and roll the pair of dice at the same time. For the coin, if it turns out to be heads, we will get two points. On top of that, we will get points equal to the sum of two numbers from each dice. Let us define a sample space, S, as all possible points we can get.
Let us assume the coins is fair coin also both the dice are fair. Note that both the events of tossing a coin and rolling two dice are independent of each other. We denote T for getting a tail and H for getting a head. Suppose (x,y) be a outcomes for rolling two dice.
We know that after rolling two fair dice, the sum of number on two dice could be one of the number from {2,3,4,5,6,7,8,9,10,11,12} so the points could be one these 11 outcomes. We get 2 points for each head and nothing for a tail.
Suppose we get head on the coin then on total we get one of these points {2+2,3+2,4+2,5+2,6+2,7+2,8+2,9+2,10+2,11+2,12+2}.
Suppose we get tail on the coin then on total we get one of these points {2+0,3+0,4+0,5+0,6+0,7+0,8+0,9+0,10+0,11+0,12+0}.
This gives we get on total one of these {2,3,4,5,6,7,8,9,10,11,12,13,14} points. Number of elements in the sample space S are, 13.
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