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What is the probability that a letter chosen at random from the 26 letters in the alphabet would be in the word mathematics?
There are eight different letters in 'mathematics' - a, c, e, h, i, m, s and t. Since there are 26 letters in the alphabet, the chance of a randomly chosen one being a letter that's in mathematics is 8/26, or 4/13.
Find the probability of this event if one of these cards is drawn at random. Selecting a U not replacing it and then selecting an M.?
The answer depends on the set of cards from which the picking is done. Unfortunately, you have provided absolutely no information on that.
What is the probability of an observation being above the mean?
For a continuous variable it is 0.5 but for a discrete variable the answer depends on the probability of the variable taking the mean value. It is half of the rest of the probability. If the discrete variable X has mean m and Prob(X = m) is p then Prob(X > m) = (1 - p)/2.
What is the probability of choosing a month starting with the letter m?
It is 1/6.
Frequency approach for probability?
Well, that's not much of a question. Perhaps you are asking: What is the frequency interpretation of probability? This is called the classical interpretation of probability. Given n independent and identical trials with m occurrences of of a particular outcome, then the probability of this outcome, is equal to the limit of m/n as n goes to infinity. If you are asking: How can probabilities be estimated given data, based on frequency approach? A table is constructed, with intervals, and the number of events in each interval is calculated. The number of events divided by the total number of data is the relative frequency and an estimate of probability for the particular interval.
