An experiment consists of drawing two numbers out of a hat one after the other containing the numbers 1, 3, 5, 6. The two numbers are then recorded as a 2-digit number. The number drawn is NOT put back in the hat before drawing the second. Do the following: List the sample space.________________________________ Let F = the event of getting a number whose first digit is odd Let S = the event of getting a multiple of 6 Find P( F and S) =____________________________________ Find P(F) =______________________________ Find P(F|S) =_______________________________________ Are F and S independent events? ___________Justify_____________ VIII (15) Let E be the event that at least two people out of 4 have the same birth month (not day). How many outcomes in the Sample space. In other words, compute n(S).________ State in words the complement of E. _____________________________ How many outcomes in the event not E. In other words, compute n(not E). ________ Compute the probability of the event not E. _____________ Compute the probability of the event E. ____________
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.
An experiment consists of drawing two numbers out of a hat one after the other containing the numbers 1, 3, 5, 6. The two numbers are then recorded as a 2-digit number. The number drawn is NOT put back in the hat before drawing the second. Do the following:
List the
Let F = the
Let S = the event of getting a multiple of 6
- Find P( F and S) =____________________________________
- Find P(F) =______________________________
- Find P(F|S) =_______________________________________
- Are F and S independent events? ___________Justify_____________
VIII (15) Let E be the event that at least two people out of 4 have the same birth month (not day).
- How many outcomes in the Sample space. In other words, compute n(S).________
- State in words the complement of E. _____________________________
- How many outcomes in the event not E. In other words, compute n(not E). ________
- Compute the
probability of the event not E. _____________
- Compute the probability of the event E. ____________
The sample space is denotes the total numbers of possible outcomes.
In this case the possible outcomes are,
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