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Classical Probability
Consider the experiment of tossing a single coin. Two outcomes are possible, viz. obtaining a head or obtaining a tail. The probability that it is a tail is 1/2, i.e. 0.5. This probability is determined without an experiment based on the principle that each of the possible outcomes must be equally likely. In reality it may not be that, for every two tosses there will be one tail. But if the number of tosses is increased, however, the actual results will approximate more closely to the one-in-two pattern. Thus, in 2000 tosses there may be 998 tails. If the probability of a tail being tossed is one in two, it does not follow that, in order to maintain the probability ratio, the next toss will produce a head.
As per the Classical approach, the probability is the ratio of the number of equally likely possible outcomes favorable for an event to the total number of possible outcomes. If there are m possible outcomes that favor the occurrence of event A and there are n total possible outcomes, then the probability of the occurrence of event A is the ratio of m to n (m/n). The possible outcomes favorable for an event and total number of outcomes must be known without performing experiments.
By pigeonhole principle, show that if any five numbers from 1 to 8 are chosen, then two of them will add upto 9. Answer: Let make four groups of two numbers from 1 to 8 like
Your grandparents gave you a gift of R2 000 on your 16th birth day. You want to invest the money in an account over four years. You have an option of investing the R2 000 at 8% per
Find the value of x if 2x + 1, x 2 + x +1, 3 x 2 - 3 x +3 are consecutive terms of an AP. Ans: a 2 -a 1 = a 3 -a 2 ⇒ x 2 + x + 1-2 x - 1 = 3x 2 - 3x + 3- x
5/7+5/14
Solve the form ax 2 - bx - c factoring polynomials ? This tutorial will help you factor quadratics that look something like this: 2x 2 -3x - 14 (Leading coefficient is
tan 2x = 1
whta are the formulas needed for proving in trignometry .
Q. How to Subtract fractions with different denominators? Ans. As with adding fractions, you can't subtract unless the denominators are the same. Here is an example: 9/
MAKING CONNECTIONS : you have read about what the ability to think mathematically involves. In this section we shall discuss ways of developing this ability in children. As yo
Standard errors of the mean The series of sample means x¯ 1 , x¯ 2 , x¯ 3 ........ is normally distributed or nearly so as according to the central limit theorem. This can be
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