1.) A student takes a multiple choice exam with 30 questions, each question has 5 answer choices. He knows how to answer 19 of the questions, and randomly guesses on the remaining problems. Assume he correctly answered the questions he did not guess. The teacher randomly selects a question for him to solve on the whiteboard. Given that he answered the question correctly, what is the probability that he guessed?
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.
1.) A student takes a multiple choice exam with 30 questions, each question has 5 answer choices. He knows how to answer 19 of the questions, and randomly guesses on the remaining problems. Assume he correctly answered the questions he did not guess. The teacher randomly selects a question for him to solve on the whiteboard.
Given that he answered the question correctly, what is the
2.)
An actuarial student studies for an exam using a review course, a textbook, or both.
- 70% of students using only a review course pass,
- 40% of students using only a textbook pass, and
- 75% of students using both pass.
- 40% of students use both methods.
- 20% use a textbook only.
Given that a student passes, what is the probability that a student only used a review course?
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