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Learn More - FAQs - Order Now!
Here on the
web site we take a look at probability. This will absolutely, certainly, positively, (yes siree!) appear on the exam. So you’d better get good at it!
When it is guaranteed that something will happen, the probability of it happening is 1. For example, the probability that the Earth exists is 1, because we’re all absolutely certain that it does.(I hope.) When we absolutely know that something won’t happen, the probability of it happening is 0. For example, the probability that you will fail your exam with the help of this web site is 0! (snigger) Therefore, all probabilities must have a value between 0 and 1. So if you end up with something having a probability of 2.5630974, you know that something’s gone drastically wrong! You can express a probability as a fraction or a decimal.Now, if you toss any fair coin into the air, you know that you’ve got a 50-50 chance that it will land on heads. The chance of it landing on heads is called the probability of a head, and the side that lands face up is called the outcome. Since there’s a equal chance, this is an equi-probable (remember this word) event. Another example is with dice, there’s an equal chance that it will land on 1,2,3,4,5 or 6.
In the following formula, P(E) stands for the probability of an event happening.
A fair coin is tossed once. What is the probability that the outcome will be heads?
Total number of "correct" outcomes = 1
Total number of possible outcomes = 2
Therefore the probability that the coin will come down heads is : 1/2
26 letter cards are placed face down in front of Tony. Tony is then asked to select a card at random. What is the probability that Tony will select a vowel?
Total number of "correct" outcomes = 5 (a, e, i, o, u)
Total number of possible outcomes = 26
Therefore the probability that Tony will select a vowel is : 5/26
If the probability that when a coin is tossed, it will come down heads is 1/2, it is not true that if you toss the coin twice, you’ll get 1 head. What it really means is that, when it’s all been said and done, you’ll probably end up with about 250 heads if you tossed the coin 500 times. Even so, you wouldn’t really be concerned if only 245 heads showed up, or if 259 did. Now look at the following formula:
P(E) = Number of trials with favourable outcomes divided by the total number of trials
Basically, what this formula means is that the chances of something happening in an experiment is equal to the number of "correct" trials divided by the total number of trials. Now here’s the don’t. Don’t ever confuse this with the formula below:
P(E) =Total number of "correct" outcomes divided by the total number of possible outcomes
The formula we're looking at now refers to an experiment that is repeated many times, e.g. 200. However, the formula directly above refers to single events in probability, i.e. we throw a dice once to see whether we will get a certain number.
100 footballs are checked for punctures. If 20 footballs are found to have punctures, calculate the probability of a football having a puncture when chosen at random.
P(E) = Number of trials with favourable outcomes divided by the total number of trials
and therefore the answer is 20 divided by 100 which equals 20/100 = 1/5 (0.2) Note that a football having a puncture is considered to be the favourable event!
...........................................
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as well as Algebra, The Circle, Areas and Volumes and much, much more, get Adam's unique, All-NEW Math, Maths Buster revision study guide e-Book! 116 pages packed full of detail, content, handy hints, questions and answers and more, and written in Adam's popular light-hearted and very easy to understand style, everything you need to help you get a top grade in your math or maths exam!
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