A driver wants to drive from point I to point II. He can choose either path A or path B for his drive. Along each path, there are two signal lights that can be either green or red. The driver finds the first light to be green or red with equal probability along each path. The lights along path A are designed so that with probability 0.8 the driver finds the second light to be of the same color as the first one. Similarly, along path B, lights are designed so that with probability 0.7 the driver finds the second light to be of the same color as the first one. The driver selects a path randomly and drives to his destination. If the driver found no red lights along the way, find the probability that he chose path A
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.
A driver wants to drive from point I to point II. He can choose either path A or path B
for his drive. Along each path, there are two signal lights that can be either green or red. The driver
finds the first light to be green or red with equal
are designed so that with probability 0.8 the driver finds the second light to be of the same color as
the first one. Similarly, along path B, lights are designed so that with probability 0.7 the driver finds
the second light to be of the same color as the first one. The driver selects a path randomly and
drives to his destination. If the driver found no red lights along the way, find the probability that he
chose path A.
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