Check over your 4 basic rules before submitting your assignment:
Rule 1. Remember to first set problem into a fraction, then convert fraction to decimal, then decimal to percentage.
Rule 2: Remember if the question is asking for more than one probability, you must obtain each individual probability separately, and then combine using the and/or rule. Don’t forget to combine your multiple probabilities for your final outcome.
Rule 3: When working with problems that ask for more than one probability, remember that if it states “without replacement,” then you need to “take away” one from each following probability. If it does not state specifically “without replacement,” then you can assume that you are performing probability “with replacement.”
Rule 4: Remember the original pool of variables you are drawing from.
Rule 5: Work at least 5 spaces out to the right of the decimal.
VERY IMPORTANT HELPFUL HINTS WHEN WORKING ON YOUR PROBABILITY ASSIGNMENT!!! When you are working on your assignment, you want to focus on these things:
The commentary provides for you the step-by-step process of completing a probability question and provides for you examples for how some of the different problems will look like in obtaining probabilities.
If the question is asking for only one probability, then you compute that one probability. If the question is asking for more than one probability, then you compute each probability independently before combining (such as “what is the probability of obtaining X and/or Y?”). After computing each probability separately, you then combine them using the “and/or rule” either by adding or multiplying.
Your probabilities are first expressed as a fraction (i.e., “If you have a bucket of 10 marbles: 8 blue and 2 red, what is the probability of drawing a red marble? Answer: 2/10. Why? Because you have 10 marbles to start with and only 2 chances of drawing a red marble from the bucket). Right after expressing the problem in fraction form, you turn it into a decimal by dividing the numerator from the denominator. (2/10 = .2) before you then proceed with the rest of the problem. We do this since doing the “math” is easier for decimals than for fractions. If your problem involves more than one probability, do not combine these probabilities as fractions, but convert each individual probability to a decimal first as this is an easier to compute.
When working on questions with more than one probability involved, remember that you have to follow through using the “and/or” rule. If you simply produce a fraction or a decimal for each individual probability but then do not finish out the math, then your problem is only half-way done.
So far, rounding to 2 spaces to the right of the decimal has been acceptable. When working with probability and on, the farther to the right you round, the more accurate your outcome will be. So do not round to whole numbers when your outcome involves values beyond the decimal. It never hurts to round to 4 or 5 spaces to the right. Also, make sure that you are rounding correctly. Go back to Week 1 and review rounding rules. This will make a difference when we begin working more complicated formulas. If you round the wrong way too early, then it can throw off the rest of your calculations.
Your very last step is converting your final decimal into a percentage (i.e. “There is a 20% chance of pulling a red marble from the bucket.”). You simply move your decimal over 2 spaces to the right and then put the % symbol on the end. Without the % symbol, it is easy to confuse the value with a whole number or the proportion. This is why it is important to utilize your symbols.
If the question says “with replacement,” then that means the values you are drawing from stay constant. However, if the question says “without replacement,” that means that your values will drop one for every one draw. Make sure to make these adjustments for “without replacement” problems. Also, be sure that if you are obtaining a probability “without replacement,” double check and make sure whether or not it is just the denominator that changes (the bottom number) or in some cases, also the numerator (for instance, if you are asked the probability of pulling 4 aces from a deck of cards in a row “without replacement,” not only would your denominator change, but so would you numerator. The first draw would give you 4/52, since you have 4 aces in a deck of 52 cards. The second draw would leave you w/ 3/51, since you are not only short a card, but also short an ace due to the probability of the first draw, and so on …. 2/50 and 1/49).
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