a. A train of 14 cars is to be composed of 6 boxcars, 5 flat cars, and 3 tank cars. These are to be chosen from among the following groups: 6 boxcars from a group of 16 5 flat cars from a group of 10 3 tank cars from a, group of 8 (Assume the order of arrangement of the cars is not relevant for this part.) b. In this part we assume the 14 cars are already selected, and we are concerned with the number of different arrangements of the 14 cars. How does this number change if instead of 14 distinct cars we assume there are 6 boxcars (indistinguishable from one another) as well as 5 flat cars (also indistinguishable) and 3 tank cars (also indistinguishable)?
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.
Permutations and Combinations
examples
a. A train of 14 cars is to be composed of 6 boxcars, 5 flat cars, and 3 tank cars.
These are to be chosen from among the following groups:
6 boxcars from a group of 16
5 flat cars from a group of 10
3 tank cars from a, group of 8
(Assume the order of arrangement of the cars is not relevant for this part.)
b. In this part we assume the 14 cars are already selected, and we are concerned with the number of different arrangements of the 14 cars.
How does this number change if instead of 14 distinct cars we assume there are 6 boxcars (indistinguishable from one another) as well as 5 flat cars (also indistinguishable) and 3 tank cars (also indistinguishable)?
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