What is Your Chance of Winning the Lottery? Not Very Probable! Background: Probability is the chance of an event occurring. Scientists who do research are very interested in probability because they want to help ensure that their observations are not due to random chance. For example, if you wanted to find out if a certain fertilizer was effective, you would test it on a large sample of plants and compare it to another sample that did not receive the fertilizer. The actual probability of an event improves with sample size -­‐ the larger the sample, the more accurate the results. Scientists, therefore, use as large a sample as possible when doing research. Although people are always purchasing lottery tickets, the chance of winning big is very small. For example, the chance of winning the top lotto prize in New York State is 1 out of over 45 million! Although, the more tickets you purchase, the better your chances, you would have to spend a lot of money to really improve your chances. Probability is expressed as a percentage or a ratio. Chance of event occurring Probability =__________________________________ x 100 Total possibilities of the event Therefore, using the formula for probability, the chance of getting either heads or tails is 1 x 100 = 50% __ 2 Expressed as a ratio, it would be: 50:50. Scientists are also interested in the percentage of error or how much a value obtained differs from the expected value. They know that sample size affects the percentage of error. In the activity, you will see if the number of times you flip a coin affects it percentage of error or how much it differs from the expected value. Percentage of Error = Difference between measured value and accepted value x 100%
________________________________________
Accepted Value
Materials: one penny Probability 1 Procedure 1. Working with a partner, one person flips the coin while the other makes a tally on the heads or tails tally sheet 2. Flip the coin 10 times. How many heads and tails did you get? ________________________ 3. Flip the coin 50 times. How many heads and tails did you get? _________________________ 4. Flip the coin 100 times. How many heads and tails did you get? ________________________ 10 Tosses Heads Tails 50 Tosses Heads Tails 100 Tosses Heads Probability 2 Tails Results: 1. Using the formula for percentage of error, calculate the percentage of error for 10, 50 and 100 tosses in the spaces provided below. 10 tosses 50 tosses 100 tosses 2. As you increase the number of tosses. What happens to the percentage of error? Conclusion Why is it important to use as large a sample size as possible when doing an experiment? Probability 3