At each stop, each passenger alights from the bus, independently of the actions of others, with probability 0.2 each. Either 0,1 or 2 new passengers get on the bus, with probabilities 0.5, 0.4, and 0.1, respectively. Passengers at successive stops act independently. Assume the bus is so large that it never becomes full, so new passengers can always board. Assume that the bus is empty when it arrives at the first stop. Question:
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.
Bus Ridership
Assumptions:
- At each stop, each passenger alights from the bus, independently of the actions of others, with
probability 0.2 each. - Either 0,1 or 2 new passengers get on the bus, with probabilities 0.5, 0.4, and 0.1, respectively.
- Passengers at successive stops act independently.
- Assume the bus is so large that it never becomes full, so new passengers can always board.
- Assume that the bus is empty when it arrives at the first stop.
Question:
Say an observer at the second stop notices that no one alights there, but it is dark and the observer couldn’t see whether anyone was still on the bus. Find the probability there was one passenger on the bus at the time.
I got probability 0.4, can you verify that's correct and if not, show me what I could be doing wrong?
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Hi. Can you please explain where the actual number amounts, e.g. 0.4 and 0.8 come from? Thanks.
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